"You can not do it now and do it later." means (to me at least) "It's not possible to do it now and also do it later": like the expression "You can't have your cake and eat it", which would be better worded as "You can't eat your cake and still have it".
"You may not do it now and do it later." means the same as the above, with the exception being that "may" has a slight implication that the reason you can't do it is that you're not permitted to, rather than it being actually impossible.
Neither of them mean "You don't have to do it now". For this I would write "You can do it now, or later." (if i was trying to be as terse as possible)
For your second question, you could just say "It might happen" or "It might not happen". Each of these states that there are two possibilities - it happening, and it not happening - but implies that one of the cases is more likely: "It might happen" is like saying "It is more likely that it won't happen", and conversely saying "It might not happen" is like saying "It is more likely that it will happen". "Might" here implies a small probability.
To say "It could not happen" is totally different: this means that it is impossible. Somewhat inconsistently, however, to say "It could happen" means the same as saying "It might happen".