Yes, we do read these forums.
Yes, all platforms do not support everything possible, but you do realise that every single platform is evolving all the time and trying to keep up with them on all the details is hard work. Hard work that the developers of Qt are doing pretty well.
(I agree with Bluetooth being a pain, as I'm trying to write something with it myself. Luckily the platforms I want to run on have pretty good support.)
Next the legal questions.
You also need to understand that I have zero hours of law school or training, so getting a comment from me about licenses in third party app stores is like asking a random person on the street. Add to that the fact that some people will take anything as legal advice, and the result is that we do not really like to say anything out here.
As a general guide; and do not mistake this for legal advice, this is a random dude on the internet rambling about licenses.
I have not read what the Apple app store texts say currently, but the text used to be hostile toward open source licenses (again stress on the part where I have not read it recently, I hear they are softening the text).
Google has been more simple in the past, where LGPL Qt has been quite ok, there is even ministro that can handle the libraries for you.
So it's Apple that has been in the gray area where people without a legal degree can't say anything in any direction.
Then again, if you comply with the GPL/LGPL in providing the source/object files when someone asks, you are ok. (except if the Apple agreement says something else)
We do have a commercial option for small business coming out this spring still. The cost will be in line with what a small business / indie developer can afford. So nothing like the 350$/month you found (which is probably about correct for a pro app development license).
So assuming you want to do commercial apps, you can do open source and be prepared to give object / source files depending on the license you go with, or you can get a commercial license. Again assuming you are a small business / indie developer I suggest you wait a bit for the small business license that we have coming out in roughly the Qt 5.6 release timeframe.