Ask-An-Iman has Answer #10617 for this one:

1. According to the Shari’ah, it is permissible to marry one’s first cousin. The parents of all non-healthy and disabled children are not cousins unto one another.

2. It is not permissible to have any kind of pre-marital relationship. Any act or attitude, for example, liking, loving, etc. that may lead to a pre-marital relationship is Haraam (