I recall a long time ago a friend of mine tried this. The aim was to get the UFO numbers up to 1000 before going to Cydonia. Being on beginner, it took a very long time.
I don't think there's a time limit at all as the game basically lets you play on and on for many years. You will lose the occasional country to infiltration. In fact you might end up losing all of them to infiltration except Russia - though if you've reached this point you will be able to sustain yourself easily through captured equipment alone, and the loss of most of the countries lessens the impact of infiltration missions. You will still need to keep your scores up though.
Alien appearance probabilities will be based on the very last table in:
As for the PSX Game, most definitely yes. It's actually the most polished version of the game available - except for the extremely long load times, limited save capacity on the memory card, and the loss of the painted aircraft images in the ufopaedia (replaced with less impressive spinning 3d images).
NKF, wordmakeupper extraordinaire.