the males should be removed at about 4 months if you are wanting unfertilized eggs or to breed pure-breds. if that doesn't matter, then you can just leave the males. fertilized eggs will only start to develop under the right set of conditions, so if you are collecting them everyday they are just fine to eat.
the picking could be crowding or boredom or the wrong kind/amount of light or several other things. try a red light if you haven't already. make sure they have plenty of space and food. if it continues, you need to remove him.
brooding is when a hen gathers a clutch of eggs of decides to sit on them. a lot of chickens don't get broody, but some still do. they will lay eggs over several days, often hiding them, and then start sitting on them. if you aren't collecting those eggs daily you may end up with a broody hen. in that case, you have to "break her up" by removing the eggs (she won't lay while she's broody) or let her hatch them. don't eat eggs that you think have been sat on for a few days (well, i wouldn't but some people do).
yours should be roosting by now, if they want to. just offer them roosts and they should know what to do. if not, try placing them on the roost a few times until they get the hang of it.
again, 4 months is kinda the age to watch for when it comes to laying and breeding. some chickens will take longer, some will start early. just watch them and have everything ready for them by around 3 1/2 months, just to be safe. they shouldn't get layer feed until they are 18 weeks i think it is, or they start laying.
good luck!