Copious precum is possible. If it disturbs you, there are certain thongs you can do: avoid triggers for arousal, if not possible, take more often care of sexual release. Also different exercises for your perineum may help alleviate the symptoms. If this simple advice doesnt help, please make an appointment with an urologist. Good luck!
The answer to the first question is, no, nobody can sit on it and get pregnant that way. All the sperm would be dead if there were sperm in it at all, and that depends on how recently you had ejaculated. (The longer from having ejaculated, the less likely there is to be sperm in the pre-ejaculatory fluid.)
Don't know the answer to the second question, especially if you are young. (Hormones, you know.)