1.) What are some of the critical spots that I should check to make sure that everything really does work as it should.
It would probably be better just to check everything. video ports, all usb ports, wireless and wired internet, DVD player, BluRay player(A game should work fine for this), and a ps2 game are all of the things that I can think of off of the top of my head that you should probably check
2.) This PS3 Media Server was a great idea. Are there any other special things that you all do with your PS3's?
I installed Yellow Dog on mine. I eventually plan on doing ps3 development, but I am lazy and a ps3 optimization presentation that I read made my head spin.
3.) How do I make sure that my PS3 lives for as long as possible?
Just take good care of it as you would any other system. Keep it well ventilated, don't keep it on all the time, and occasionally clean the air holes (which I really need to do).
To prevent accidentally keeping your ps3 on there is a neat little feature that will turn the system off after X hours of no input. I highly suggest turning that on.