Good gracious, man, that's a lot of questions squished together into one thread. I'll try to answer them:
1) No, the clutch (weak and will probably need to be changed soon after purchase), tranny (synchros go bad, but there's a TSB - only useful if under original warranty), and t-case (known to break easily, especially if abused) are not reliable on the 03.
2) Other weaknesses would be the tire wear (you'll need new tires on a used 03 and again every 15k miles or so - $250/tire for stock Advans), the aforementioned drivetrain parts, and brakes (will need to all be replaced on a used 03).
3) One thing you'd need to know is that the Evo has NEVER BEEN MODDED. I don't mean to see if it no longer has mods, but rather to make sure it has NEVER BEEN MODIFIED AT ALL. I help people on almost a daily basis who have issues related to a previously-modified used Evo that was sorta put back to stock before being sold. Do not touch it for 21k if it's been modified in any way.
4) The warranty is over in April like you said, so although it's transferrable, it's not useful except for the next month or two.
5) I haven't dealt with extended warranties before, but Mitsu is notorious for not honoring warranty claims even on STOCK Evos. Modded Evos usually get kicked right out of the service dept.
6) We have a very well-defined set of mods that are best for a new Evo owner. You can find 2 stages of suggested mods here at EvoTuners, and I also have my own packages that I've developed for the VIIIs and IXs. I don't sell them, but my sponsors do. You can ask me about them via PM.
7) 03/04s are the slowest of the USDM Evos, but they are capable of 13.3-13.4 stock at around 101-102mph. Most people don't accomplish that, though, so you often see high 13s from stock 03s.