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Basic JQuery syntax: What mechnaic is at work in this small (2 line) piece of JavaScript / JQuery

So here' s the piece of code. I'm very new to JavaScript so don't be afraid to explain the obvious
$(".my-css-class").on("click", function() {
($(this).attr("data-property-1"), $(this).attr("data-property-2"), this);
});
There's an element in the .jsp page that looks like this:
<i class="clickMe"></i>
I know the .jsp creates a link-icon, and that the above JavaScript is an event handler. I know that it passes these 3 values as arguments another JavaScript method:
function doStuff(prop1, prop2, obj) {
if (prop1 == 'foo') {
//do stuff with prop2
}
else{
// do stuff with obj
}
}
It all works fine. What I want to know is what exactly is going on to make it work? I can't find anything in the code that connects what the event-handler returns to the 'doStuff' java-script function.
The names are totally different, so it's not reflection, it can't be parameter matching because there's other functions with the same number and type of parameters in the file, it can't be convention based because it still works if I find/replace the name of the function to gibberish.
I guess basically I'm asking what this line is doing:
($(this).attr("data-property-1"), $(this).attr("data-property-2"), this);
tl;dr: I'm at a loss, I know how the properties get as far as the onClick event-handler's anonymous function - but how does JavaScript know to pass them as arguments the to the doStuff() function?

the onClick event is a standard event triggered on click of any clickable html element and is automatically raised by the DOM.
You are hooking in to this by listening on any matched ".my-css-class" elements for an onClick Event.
The jquery syntax ".on" has been simplified over time and allows you to hook into any number of events like "submit" - OnSubmit event , or "load" - onLoad Event
Wherever your on("click", myFunction) event hook is picked up, your myFunction will execute.
Looking at your second point...
because it still works if I find/replace the name of the function to gibberish.
The DoStuff function will be found and replaced across all files in your site? or page? or open tabs? , so therefore it must exist somewhere as "doStuff(" or "giberish(".
so when you do a global find/replace, do each one slowly, until you locate it.
Finally, when you do a view source in the browser, this should either explicitly show you the doStuff function, or at the very least give you a clue as to satelite files loaded at runtime, where you can go and investigate.
Use firebug in firefox to debug loaded resources; the ".net tab" to view external loaded resources and the html/javascript they might contain. (for example: your master page might be loading in an embeded resource that contains the doStuff method, becuase of a user or server control reference in that master page)
Also have a look at this:
http://www.developerfusion.com/article/139949/debugging-javascript-with-firebug/
You can step through the javascipt piece by peice until it hits the doStuff method.
Just remember to set at least 1 breakpoint ;-)

Dynamically Included Javascript and Dependencies

So, as a sort of exercise for myself, I'm writing a little async script loader utility (think require.js, head.js, yepnope.js), and have run across a little bit of a conundrum. First, the basic syntax is like this:
using("Models/SomeModel", function() {
//callback when all dependencies loaded
});
Now, I want to know, when this call is made, what file I'm in. I could do it with an ajax call, so that I can mark a flag after the content loads, but before I eval it to mark that all using calls are going to be for a specific file, then unset the flag immediately after the eval (I know eval is evil, but in this case it's javascript in the first place, not json, so it's not AS evil). I'm pretty sure this would get what I need, however I would prefer to do this with a script tag for a few reasons:
It's semantically more correct
Easier to find scripts for debugging (unique file names are much easier to look through than anonymous script blocks and debugger statements)
Cross-domain requests. I know I could try to use XDomainRequest, but most servers aren't going to be set up for that, and I want the ability to reference external scripts on CDN's.
I tried something that almost got me what I needed. I keep a list of every time using is called. When one of the scripts loads, I take any of those using references and incorporate them into the correct object for the file that just loaded, and clear the global list. This actually seems to work alright in Firefox and Chrome, but fails in IE because the load events seem to go off at weird times (a jQuery reference swallowed a reference to another type and ended up showing it as a dependency). I thought I could latch on to the "interactive" readystate, but it doesn't appear to ever happen.
So now I come asking if anybody here has any thoughts on this. If y'all want, I can post the code, but it's still very messy and probably hard to read.
Edit: Additional usages
//aliasing and multiple dependencies
using.alias("ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js", "jQuery");
using(["jQuery", "Models/SomeModel"], function() {
//should run after both jQuery and SomeModel have been loaded and run
});
//css and conditionals (using some non-existant variables here)
using.css({ src: "IEFix", conditionally: browser === "MSIE" && version < 9 });
//should include the IEFix.css file if the browser is IE8 or below
and to expound more on my response below, consider this to be file A (and consider the jquery alias from before to be there still):
using(["jQuery", "B"], function() {
console.log("This should be last (after both jQuery and B have loaded)");
console.log(typeof($));
});
Then this would be B:
using("C", function() {
console.log("This should be second");
});
And finally, C:
console.log("This should be first");
The output should be:
This should be first
This should be second
This should be last (after both jQuery and B have loaded)
[Object Object]

Commendable that you are taking on such an educational project.
However, you won't be able to pull it off quite the way you want to do it.
The good news is:
No need to know what file you are in
No need to mess with eval.
You actually have everything you need right there: A function reference. A callback, if you will.
A rough P-code for your using function would be:
function using(modules, callback) {
var loadedModules = []
// This will be an ajax call to load things, several different ways to do it..
loadedModules[0] = loadModule(modules[0]);
loadedModules[1] = loadModule(modules[1]);
// Great, now we have all the modules
// null = value for `this`
callback.apply(null, loadedModules);
}

open url using javascript

I need a way to load a website - something like gBrowser.loadURI, window.location or window.open - but I need to execute some more code AFTER that website has been loaded (and parsed by the browser). The functions I've mentioned don't block execution of my code until the site is fully loaded, but only until it has started loading.
In case it matters: This code will not be part of my/a website, but will be a FireGestures script.

https://developer.mozilla.org/en/Code_snippets/Tabbed_browser#Manipulating_content_of_a_new_tab seems to be what you want. They suggest:
var newTabBrowser = gBrowser.getBrowserForTab(gBrowser.addTab("http://www.google.com/"));
newTabBrowser.addEventListener("load", function () {
// use newTabBrowser.contentDocument to manipulate DOM
// or do whatever you want on-load
}, true);
See also docs for tabbrowser and browser.

Page Initialization: Does one need onload?

Regarding this SO article and this SO article. I looked at these after noticing my web app does not fire in IE8...I don't care about backward compatibility at the moment but if it's one line of code why not? Anyways the other issue I was having is the onload event waits for all the content to load...so the user has no controls if he/she is waiting for images to download. This led me to believe that I should just use
<script type='text/javascript'>my_initialize_function()</script>
placed in the html where I want the page to initialize.
and say to bye to
window.onload = initializePage;
or
window.addEventListener('load',initialize_page);
or any similar.
My question is: Is this a valid approach to initializing one's page?
PS: I'm not using any libraries including JQuery...and obviously I would not try to initialize elements that have not been loaded yet.

No.
jQuery and similar libraries has an interesting approach. They simply capture different events in a crossbrowser manner while making it easier for the developer to use.
Let's consider the following code:
<script> document.getElementById('a').innerHTML='b'; </script>
<div id="a"></div>
It may or may not work depending on whether the browser runs javascript when it finds it or only after the whole document has been built.
On the other hand, if you used the proper event mechanism but the document has already been built, your code will not be called.
jQuery unites both paradigms to get a seamless and better system. Something like so:
var foo = {
// holds list of callbacks to call when document starts
stack: [],
// document not ready yet
ready: false,
// add callback to be called when document is ready
add: function(callback){
foo.stack.push(callback);
if(foo.ready)foo.fire(); // document is ready, call fire
},
// fire callbacks (document IS ready)
fire: function(){
for(var i=0; i<foo.stack.length; i++)
foo.stack[i]();
foo.stack = [];
foo.ready = true; // document IS ready
}
};
// bind to browser events
window.onload = foo.fire; // TODO: you should use actual events
// example of use
foo.add(function(){
alert('Document is ready!');
});

You could use jQuery's $(document).ready() event. It fires after the DOM is complete, but before all images are loaded.

Javascript executing when jQuery not ready

The following scenario is a problem I am having. I came to the conclusion that jQuery must not be ready when Javascript is executing by observing this scenario.
Scenario:
I have a Java application which injects Javascript script tags into the currently loaded DOM page. The following Java code runs inline Javascript which inserts jquery.js and myCode.js. myCode.js holds my Javascript codes.
browser.executeJavaScript("var head= document.getElementsByTagName('head')[0];" +
"var script= document.createElement('script');script.type= 'text/javascript';script.src= 'jquery.js';head.appendChild(script);" +
"var script4= document.createElement('script');script4.type= 'text/javascript';script4.src= 'http://myCode.js';head.appendChild(script4);");
In this Java application, I also have a buttonListener that fires a function in myCode.js in ActionPerformed();
executedJS = browser.executeJavaScript("replaceAllLinks()");
The problem that is encountered is nullPointerException at the above line when button is clicked. Accomodating for null case results in endless loop without any changes.
while(executedJS == null) browser.executeJavaScript("replaceAllLinks()");
The cause of the problem was pinpointed down to when jQuery functions, methods are present inside replaceAllLinks(); javascript function. when jQuery, methods were absent, no problems could be observed. There was not one instance of nullPointerException raised.
The only possible underlying issue would be that somehow jQuery library is not fully loaded while replaceAllLinks(); is being executed. If jQuery methods and functions were not in use, it doesn't matter and everything runs okay.
My question is then, how can I make sure that jQuery is fully loaded and available for use?

Every script relying on jQuery should be contained inside a DOM ready function. Such a function normally takes this form:
$(document).ready(function() {
/* code here */
});
and a shortcut to achieve the same thing would be:
$(function() {
/* code here */
});
Here's the documentation for further information on the ready method:
http://api.jquery.com/ready/

Declare some global variable at the end jquery.js, e.g.
window.jQueryIsLoaded=true;
and check this variable before using jQuery.
<edit>Forget this, see Salman A's comment below, should be the right answer.</edit>