First and foremost, I can glean from your question that your unit is an iPhone 4, and not an iPhone 4S. However, you should give us the last four letters and numbers of the serial code.
1. No one can tell that for sure. The only way to know is changing the battery, booting up the unit and tell how it goes. You may also want to clean it more throughly with isopropylic alchol.
2. Not that I know. If you go through the iFixit site, you may see that several key parts of the iPhone 4, including the bezel mount and some of the assembly, are radically different, thus...
3. ... you can't "upgrade" your unit.
You could, however, if your current issues are "just" a really short battery life and your unit heating try to fix it by buying a new battery only, and ordering a new logic board only of other troubles arise.
It's a safe bet saying that the plunge in water shorted up the battery, and will account for a short battery life and the heating up device (the logic keeps trying to charge a broken down battery).
The rest... has to assessed later, or in a professional lab.
If you're handy enough to do it by yourself, the safest course of action is:
- Acquiring some isoprophylic alchol
- Dismantling your unit, cleaning up gently the logic board and pay attention to suspicious patches of rust and other water debris, scrubbing them really gently
- Let the alchol dry: it dries much faster than water, that's why it has to be used
- Replace the battery
- Close the device, reassess the damages
- Eventually, report here how your iPhone is holding up
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