1. You can keep him prisoner so that he won't go around destroying you any more, or you can wait to get a ransom offer from his faction, and if you have a castle/town you can put him in the prison so he is less likely to escape, and to free up your prisoner limit. (Just a little advice I always like to keep him and reject the ransom so that he won't be able to build an army and continue to harass me, and my faction besides the ransom offers aren't that high any way)
2. You can't start with a lance, well at least I'm 99% sure you can't
3.Well you have to aim DIRECTLY at the enemy and you have to be going fast enough on a horse so if you get stopped by massed infantry you're pretty much dead. I suppose it could also be that lances aren't too good for anything but couching
I honestly can't think of too many disadvantages.