I admit, I'm not a wizard when it comes to understanding the spiritual essence of computer's personal life, so I' just ask you then...

Does increasing screen resolution also increase video card's temperature? Does it increase processors inner warmth?

What might be the "beware, I'm about to melt..." temperatures for GeForce 9800 GT and AMD II X4 processors?

1) NVidia makes monitoring software for this very purpose. Go to their site and install it (or find the equivalent on your mobo's website).

2) 9800 GT ran very hot, you could cook an egg with that SOB.

3) 9800 GT was kind of overhyped, if you need you can replace it with a far better card for around 60 bucks.

EDIT: yeah it'll increase the heat, I don't know if it's by an appreciable amount though.

Are you talking about 2d or 3d?

In 2d its shouldn't make any difference whatsoever. 3D likely will but I've never benchmarked it so couldn't say for sure.

Temperatures for GPUs can usually go well above 100 degrees safely, obviously it varies between models

Not usually, and if there is an increase, it's usually so negligible that you don't need to worry.

JUST make sure you case is clean and well ventilated. Hot, dusty air kills your components much faster then high temps.

Yes, dust is the number 1 killer. Especially when it builds up in heatsinks.