Well, as long as your computer is N-series ready, your computer hardware spec should make no difference to the ping, only the ISP should effect what the ping is like. Plus N-series only affects wireless, it should not affect cable connections.
Yes, hence why computer hardware never make your ping lags, the other form of lag come from g-card, call the FPS (Frame Per Sec) lag, that makes the game jitter as well
Yes, it makes your g-card overheats and make your FPS drops if cooling system is bad, it can also lead to crashing. Of course it doesn't just affect your g-card, it will also affect your processor, but generally overheating processor is slightly harder but possible.