Internal Bluetooth Failed in Mac Pro
Your question contains a myriads of questions, but let me try to give you a hint on some.


Possibly not, unless you can find a way to fix it, Apple will happily charge you fix it for you.
I don't know if it will be better, but I know that the BT on that machine works ok. And that's because I have the exact same model. Mac Pro early 2008 with Dual Quad-Core Xeons in it.
Yes and no. I've used the (included) Mighty mouse for a week. I hated it and simply gave it to a friend who liked it. There IS some latency in BT peripherals and there are some micro-disconnections that get fixed real fast, but if you're playing a FPS, you'll notice a small "it's not working" moment. Also, the less change the batteries have, the more this will happen. Same with the keyboard. You're typing and then ……… a couple of secs of nothing and then it works again. Sometimes you even get the "Disconnected" Bezel on screen.
I can't help you with that. I absolutely hate mighty mice. 


The plural of mouse is mice ;-)