I am sorry for you having major troubles with your phone. The quantity of problems seems like these are not only software related.
3) Try and take off the screen itself for re-mounting it if you are able to. Help for doing this can be found here in this forum and on "ifixit". This action has helped some in the past.
4) Maybe try the same for the speaker module, therefore the entire phone is build in a modular design. Could help too.
6) Now you know why you battery drains so quickly. This permanent connectivity for synching is heavy duty, which brings me to no.7
7) NO, it surely is not, unless it is somehow broken! This is a false statement as several FP2 users here can prove as wrong me including. My last full battery charge from thursday lasted until yesterday without "battery saver" active. But I do not permanently synchronize and don´t have any Facebook app installed. Furthermore I have a close look into the "battery" monitor which apps are running maybe wasting my battery. You also should take a look into this settings->battery; and also ´running´ apps in settings->apps->running. I do look out for proper acting apps, not only mainstream apps. Facebook app is known for causing major troubles due to bugs. This can also be read here in the forum. Some other users deinstalled it to recover the phones reliable operation again.
8) I assume this rather depends on your chargers power rating (usb cable quality) being able to deliver enough current to charge your empty battery AND pull up your phone. Have this checked first before giving maybe false statements. There is a lot of information to be found here in this forum.
Generally you may also get back to the customer service of FP for further help and assistance.
Before returning it a factory reset could revolve issues as well.
This is your judgement. But keeping your wifi/data connection permanently active is one of the most power hungry parts beside the screen.
Generally I believe coming through one day with one charge should not be hard if not using heavy-duty apps or maybe games.
Some users here who have switched to FP2 complaint with their previous phone they could easily come through one day with one charge, I do see how often non-FP users actually plugin during their work-day....but if that is true it could also be a solution. Luckily switching phones works back and forth.
I know there are models out there lasting long, but as the battery performance is an issue very often in official tests and user-experience e.g. Amazon I think it is still the minority.