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Prevent Specific JS Loaded by iframe from Running on my Site

I want to know if it is possible to block JS, loaded by an iframe, from running on my Wordpress site. I currently embed iframe generated by a service I pay to use for my business. The iframe comes with Google AdSense ads embedded in it. Recently, the rogue pop-ups have been affecting my customers. Essentially, these are ads that run on the mobile version of my site and initiate a series of redirects. I can prevent these on my own device with an AdBlocker, but not all of my customers are that savvy.
I have tried to disable the Google AdSense ads a few ways: CSS display:none; (fails, as the JS is loaded even if the element is hidden with CSS), PHP (created a plugin that leverages wp_deqeue_script, targeting the google ad script files (blocks some JS, but ultimately fails to prevent every instance of the ads), and even HTML in the head section of my site, (the idea is that it prevents loading sources outside my domain, fails).
Is there a way to programmatically prevent these JS files from loading on my site?

There is not so much you can do about it. As #charietfl states in the comment you should think in the first place about not embedding this at all if that is a possibility for you.
From programming perspective there is only one reliable thing you can do: use iframe sandbox mode.
https://developer.mozilla.org/en-US/docs/Web/HTML/Element/iframe
This way you can prevent the IFRAME target from running ANY scripts - I do not know though if its a valid scenario for you. Otherwise there is actually no reliable way to affect the loaded iframe.

How to deal with AdBlock blocking non-ad elements

I recently had an issue whereby a user was complaining that they couldn't access a certain page because the link wasn't where it was supposed to be.
After some head-scratching, I had them disable all browser extensions and sure enough the problem went away. Re-enable extensions one by one...
AdBlock.
For some reason, it was blocking the links to the pages the user wanted to access.
Now, I don't run ads and never plan to, so usually I just tell people with this problem to whitelist the site and all is well. But if someone never knew there was a problem to begin with, I would actually lose traffic because of this. So how can I avoid this?
The only thing I can really think of is to detect AdBlock and pop up a small notice explaining that AdBlock is known to corrupt the website and that, since we don't run ads, they may want to disable it for the site. I mean, the site is a game, and this isn't the first time a browser extension has broken it, but I don't think first-time visitors would be too happy to see a popup asking to disable their blocker, you know?
So any solution that would actually prevent AdBlock from corrupting the site in the first place would be great.

You cannot prevent Chrome extensions from running. They operate in their own separate thread, with a privileged API, and hidden from page scripts.
Detecting adblockers is awkward. The easiest way is to create a 'sacrificial element' - a div with a class like 'ad_unit', for example - add it to the DOM and then wait a frame to see if it has been hidden (with display: none, for example, or a getBoundingClientRect check).
Element checking is tricky, though, because strictly speaking there's no guarantee an adblocker will run synchronously or before your checking code.
Because adblockers run in a privileged mode, their operation does not trigger events in the nonprivileged script space. To put it more simply: you can't use DOMMutationEvents to spy when a foreign extension messes with your page.
The other option is to try and load a 'sacrificial file' - an image with a URI that looks like an advert, say - and then attach an onError handler to the element. If it throws an error that looks suspicious (I think it's ERR_BLOCKED_BY_CLIENT on Chrome), then you show your warning message.
Your final choice is to try and avoid incurring Adblock's wrath in the first place. Adblockers generally use open blacklists of URIs and CSS selectors, like EasyList (https://easylist.to/easylist/easylist.txt) - this is what AdblockPlus uses and a fair few others. You could just try and make sure your DOM elements never have IDs or classes that collide with any of those selectors. It's a big list, though, and it can change at any time.

Chrome extension content script issues when extension is disabled

When I disable the extension that I am developing, the content that I injected remains on the page (and things get messy since the JavaScript is no longer hiding the content). Is there a way that I can recognize the event and reload the page when it is disabled?

Yes its possible to detect the situation, thou i think its fine if the user needs to refresh manually uppon uninstall/disable.
One way is to regularly message your extension from the injected script to check if its still alive. I do this for an extension of mine to detect when chrome updated it, which has similar consequences as the old version of the background script goes away without notice and the content script is left orphan.

Unfortunately, I don't think there is - somewhat by design. Extensions are intended to run on top of web pages, and the web page shouldn't typically modify its behavior for extensions. This abstraction, though, results in web pages being unaware of an extension's running state.
If you are the one disabling the extension, you could make a "clean up" method which refreshes all pages on which the extension is running, but you'd have to manually trigger that prior to disabling it.

Automated conditional browsing in background with chrome extension

I am researching the possibility that I might be able to use a Chrome extension to automate browsing and navigation (conditionally). My hope is that the extension can load a remote page (in the background) and inject a javascript to evaluate clickable links and click (by calling the click method) the appropriate (evaluated by some javascript logic) link, then repeat process for the resulting page.
My ability to javascript is not the problem - but I am struggling to discern whether (or not) a chrome extension can load pages in the back and inject script into them (making the DOM accessible).
I would be pleased if anyone could confirm (or deny) the ability to do so - and if so, some helpful pointers on where I should research next.
#Rob W - it seems the experimental features fit the bill perfectly. But my first tests seem to show the features are still very experimental ... ie. no objects get returned from callbacks:
background.html
function getAllosTabs(osTabs){
var x = osTabs;
alert(x.length); // error: osTabs is undefined
}
function createOffScreenTabCallback(offscreenTab){
document.write("offscreen tab created");
chrome.experimental.offscreenTabs.getAll(getAllosTabs);
alert(offscreenTab); // error: offscreenTab is undefined
}
var ostab = chrome.experimental.offscreenTabs.create({"url":"http://www.google.com"}, createOffScreenTabCallback)
alert(ostab); // error: ostab is undefined
Some further digging into the chromium source code on github revealed a limitation creating offscreenTab from background:
Note that you can't create offscreen tabs from background pages, since they
don't have an associated WebContents. The lifetime of offscreen tabs is tied
to their creating tab, so requiring visible tabs as the parent helps prevent
offscreen tab leaking.
So far it seems like it is unlikely that I can create an extension that browses (automatically and conditionally) in the background but I'll still keep trying - perhaps creating it from script in the popup might work. It won't run automatically at computer startup but it will run when the browser is open and the user clicks the browseraction.
Any further suggestions are highly welcome.

Some clarifications:
there's no "background" tabs except extension's background page (with iframes) but pages loaded in iframes can know they are being loaded in frames and can break or break at even the best counter-framebreaker scripts
offscreenTab is still experimental and is very much visible, as its intended use is different from what you need it for
content scripts, and chrome.tabs.update() are the only way handle the automated navigation part; aside being extremely harsh to program, problems and limitations are numerous, including CSP (Content-Security-Policy), their isolated context isolating event data, etc.
Alternatives... not many really. The thing is you're using your user's computer and browser to do your things and regardless of how dirty they are not, chrome's dev team still won't like it and will through many things at you and your extension (like the v2 manifest).
You can use NPAPI to start another instance chrome.exe --load-extension=iMacros.

Want to use browserAction and pageAction at the same time

Documentation says we can have only browserAction or pageAction not both. Is there any trick for this? Or as solution is this good idea to use content script and insert button in a page?

There's no mechanism for a single extension to have more than one UI element in Chrome's chrome. You could certainly inject code into a page, and present some UI there, but you won't be able to have both a browserAction and pageAction in a single extension.
You could, on the other hand, have two extensions which communicate with each other via message passing. See chrome.extension.sendRequest for details as to how that might work.