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Why and how does firefox reveal its user is in a private mode?

I use firefox and browse a link from this website. It easily detects whether I use private mode and then it blocks me if I am in the private mode.
I searched on stackoverflow.
This answer says it is impossible. But, this website has made it possible.
Another answer suggests
var db = indexedDB.open("test");
db.onerror = function(){alert('Firefox PB enabled')};
db.onsuccess =function(){alert('Not enabled')};
And this method works fine. Although, I am not sure if the mentioned website uses the same technique.
Then, I am wondering about two questions:
1- Is this the only way to detect the private mode in firefox?
2- Why does firefox stab back its users? Is it a part of its design or is it a bug in firefox?

See this bug report. Reading that should answer you second questions. They know the problem, have tried to work on it, but clearly without success up to now. Some developers think it's stupid to make indexedDB (partially) work:
Don't expose the API if every operation is going to fail.
As for your first question. There are other methods, and most browsers seem to be susceptible. Here's an article from February '19: Google wants to make it harder for sites to detect that you’re using Chrome’s Incognito Mode.
I want to add that every website has the right to refuse visitors for whatever reason they see fit. Visiting a website is not a right, it's a privilege. Your link to the joplinglobe.com for instance, doesn't work for me because I am in Europe. This happens on a lot of sites in the USA. The reason is that they want to track users in a way that is not compatible with European law (basically: Tell people what you do, and provide or remove personal data when requested), it is easier for the sites to block access to visitors they don't care about than to spent a day thinking about the privacy of their visitors.

Using SSDP to display all devices in network

I have googled this question quite often but am still a little confused as to whether what exactly I'm trying to do is possible or not.
Basically, I am trying to add a dropdown menu to my web application in which it lists all devices connected to the network. When I say devices, I'm not talking about all devices; I am talking about certain hardware devices that I am using in which SSDP is implemented. I have already created Node.js programs that send M-SEARCHes and successfully find all the devices but I understand that Node.js is not a browser javascript and there is no way I could display the output of a Node call in a terminal on a browser (please correct me if I am wrong).
After doing a bit more research into it, I realized that alternatives when doing something of this sort on a browser is to either create some sort of Chrome extension that is able to do SSDP and send M-searches, or to open websockets using a websocket API (don't think this is particularly useful in my case for SSDP but I may be wrong).
Given what I am trying to do, are either of these alternatives helpful. Is what I am trying to do even possible? Once again, I have done my research in this topic but I really haven't been able to find a clear answer. If it is possible, I'd really appreciate links to tutorials or just general ideas on how to accomplish what I am trying to do.
I know I posted something on StackOverflow recently about this, which got no answers or replies, but I have done more research into this topic and felt like I do have a better understanding. That being said, I'd still appreciate some direction as to how to approach this problem as I haven't found anything too useful online.
Thank you for your time!

Chrome extensions cannot access the sockets.udp API as far as I know. The right place to do that in Chrome would probably have been a Chrome App, as they can do UDP Multicast: https://codereview.chromium.org/12684008/ . In fact there seems to be an SSDP app already ...
Unfortunately Chrome Apps have been deprecated in favor of normal web apps (outside of Chrome OS at least), and as you've found out you can't do SSDP through normal web APIs yet. The socket API is under works but there's no telling if and when they might solve the security problems inherent in allowing a random web app to do things like join a local multicast group.
Websockets are unlikely to provide what you need.

Its possible.
Node.js is not a browser javascript and there is no way I could display the output of a Node call in a terminal on a browser
They both run Javascript. Run your nodjs in a terminal or pipe the output to a text file if terminal is not accessible. in both cases console.log() should be able to print out.
For SSDP on client and server side, use this : https://www.npmjs.com/package/node-ssdp
You need not use a Chrome app specically. You can write apps in Javascript based cross platform frameworks like Electron. Itll become a fully functional 'web'-app for PCs and for mobiles you can use Cordova and the likes.

Layout problems in CRM for Outlook

I just realized that what is a nice and working layout of a form with a webresource in on-line version, looses some (but not all) of the formatting when accessed via Outlook. It looks ugly and, I also get errors.
It's somehow related to the JavaScript added to the solution. Or, rather, the web resources, I'd say. Any suggestions on how to debug? F12 doesn't show the console when run from Outlook. I haven't done much with that version so any hint might be of help.

Are you able to narrow down your problem to a part of the script? Could you for instance disable and enable parts of the script(s) to see what works and what does not?
Since the layout is also being influenced, I think you are doing some (or a lot of?) DOM manipulation. This page on MSDN states:
HTML DOM manipulation is not supported
But there should not be that much of a problem (heard that one before...) using Outlook: Dynamics CRM 2011 Outlook client and browser rendering
Edit:
Just to prevent people overlooking the link to a related post from the comments: Random JavaScript Errors in CRM 2011 Outlook Client

Although the page you see in the CRM-Outlook is indeed rendered by IE, it's being served from another version of the engine than what is used to browse. During the rendition process it's "picturized" (lacking a better word for it) so what you see originates in a webpage but isn't one.
I don't think there's a way to debug that version. You can only rely that the development you've tested will work as supposed to. Note that there's no connected process of IE run at the same time as the Outlook client.
I'll gladly stand corrected but as far I've tried (and I've tried a lot, a lot), there's no way to get there.

JavaScript sound synthesis

As part of a third level project I am going to attempt to build a web based sound synthesiser using HTML5 and JavaScript.
Does anyone know of any APIs that would allow me to deploy it on all or most browsers?
I have so far seen an API that works with Firefox only and another on GitHub that works with Chrome only.
It would be great to be able to use this in Safari, as with the iPad it could become a stand alone instrument.
Is this feasible?

If you go to http://caniuse.com they will tell you if a technology is supported by Safari or not. Go check it out. Then, any API that you use will tell you what support you will get for it.

I think your best bet might be to do it server side. I would have your app use AJAX to call a server-side script to generate the sound file if it doesn't already exist, then return it's URL so you can use it in JS. Eventually, all the different sound files should be created by the server and named properly allowing you to look them up quickly.

http://mohayonao.github.com/timbre.js/ seems pretty powerful. Pity some of the documentation appears to be in Japanese only!

WebPd is a partial Puredata port to JS - https://github.com/sebpiq/WebPd - it works well with Chrome and Firefox. "It is also a standalone DSP library. Every object as you know it in Pure Data exposes a complete API, allowing developers to control everything with JavaScript."

Adding WYSIWYG to a site that is not your own?

This website that I use has a WYSIWYG that ONLY works in IE. And I refuse to use IE or to tell my non-tech team to use IE.
I was wondering if there is a user script or browser plugin that would enable anyone to inject a WYSIWYG such as CKeditor.com onto any site textarea?
Edit: I would also be willing to work on it myself if anyone wants to help or give advice. We could then post it on userscripts or something ...

Since you don't have access to the code, anything you do will be a hack.
With that in mind, I would start looking at Greasemonkey. It is a firefox plugin that allows you to inject javascript code into any web page on your machine. Its a long road, but that's probably your first step.
One word of warning however: While I share in your dislike of IE, it sounds like your hatred has grown to the point where it is being counterproductive. Seriously consider whether what you are about to do is worth the effort.

You can use this extension in Firefox as long as you get at least a textarea in that CMS: https://addons.mozilla.org/en-US/firefox/addon/6147/

Would a Firefox extension that displays websites as if they were in IE do the trick?

I like Stargazer712's answer (look into Greasemonkey), but there is another option.
Suck it up and use IE for just this site.
Hey, I hate IE6 and 7 as much as the next Web developer. I advise non-techies to stay away from it, and to use Firefox or Chrome. My answer isn't meant to be flip or funny.
Sometimes, if you need to get the job done, you choose the best tool for the job (even if you don't like using the tool) to get the work done in the most efficient manner possible. In this case, it sounds like using IE to access this particular Web site takes care of the problem without a single line of code or documentation written on your part.
The alternative is spending hours finding (and testing -- because you won't be the only user) an alternative...or worse, spending hours or days developing (and, again, testing) your own code to fix the problem that, at the end of the day, is really only caused by your strong dislike of the one software application that works.