Your question contains a myriads of questions, but let me try to give you a hint on some.

1. Possibly not, unless you can find a way to fix it, Apple will happily charge you fix it for you.

2. 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.

3. 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.

4. I can't help you with that. I absolutely hate mighty mice.

_{The plural of mouse is mice ;-)}

Batteries are loose

Apple designed the Magic Mouse battery compartment according to the official specification for AA batteries. Unfortunately, while Apple engineers were quite precise, the manufacturers of batteries are not. In practice, batteries vary in size, just enough to be problematic in the Magic Mouse.

Given that the batteries are hanging inside the mouse with only the tension of the terminal receptacles to keep them in place, incorrectly sized batteries can easily be pulled by gravity, falling down ever so slightly, just enough to lose contact with the electrical pads.

Wiggling the mouse is enough to re-establish contact between battery and the pads. For a while, until they fall again. Thus the annoying disconnect-reconnect-disconnect-reconnect loop.

Piece of thin cardboard

The solution is to use scissors to cut a piece of thin paper cardboard the size of the batteries. Lay this piece over the batteries before engaging the metal cover on the bottom of the mouse. The cardboard should touch only the batteries, but not the surrounding compartment of the mouse. Your goal is to get the metal door to push the paper up against the sides of the batteries, just snug enough to prevent the batteries from falling downward.

I have found the perfect thickness of cardboard to be the box enclosing a 12-pack of soda cans. A business card might do. You need about a millimeter. Thicker than sheets of paper. Card stock might do it, but may not be thick enough.