of course theres nothing wrong with that. Your both past 18 now if one was 15 and the other was 19...That's a little difference and so 4 years is perfectly normal, hey my parents are 7 years apart so 4 isn't that big a deal.
It is not wrong because both of them are adults. However, society seems to prefer the man to be older than the woman in a relationship but since this is not a rule, if the two of you like each other, then there is no reason why you should not date merely because of your age gap.
No. By this stage of early adulthood the difference caused by age is minimal. At this point it's a question of compatibility between the individuals, not their ages. The same four year difference between 16 and 20 is huge, as both parties in that case are not in the same developmental stage. One is a young adult and the other is an adolescent.