No, a doe usually has only one fawn her first pregnancy. The second pregnancy can be twins, depends on how much food is available and how much population pressure there is. A doe in an area with high deer pops., even if there's plenty of food due to farming, will often have one fawn, or even none. They have also been known to have 3 or more fawns, although that is much less common.

As to the sex of the fawns that is also susceptable to environmental conditions. The reason you see so many does to bucks is because their biggest predator, us, favors bucks in their kills.