I have a few questions about PRNGs. Maybe somebody can point me to some answers online, or even answer them here. Many thanks beforehand!

1) If a particular seed produces some sequence, say 79, 14, will 14 always follow 79 whenever 79 shows up with a different seed? I presume not, but I don't know.

2) For reasonably small N (e.g. less than 100 or 1000 for a 32-bit PRNG), does PRNG mod N behave equally "well" (as a random number) for different N? Especially, when N is very small, say 10 or 20? What about when N is a small power of 2?

Thanks again.