When you deploy vehicles that have the transport function - can you deploy them with troops already on board? Or do the troops need to board on their first movement phase?
Also, one of my "special abilities" says that in order to make my nearby units brave, I have to destroy one of my own units.
Does this mean what I think it means? i.e. My comissar kills a soldier, and everyone else is more scared of me than the enemy, so they fight harder.... (Of course it has to be a Russian... stereotypically)
(When you use this rule, do you immediately remove the unit, or does he stil get an attack that turn?)
Yes you can deploy with unit already on transport. Most important is that units can only mount or dismount on MOVEMENT phase. With the exception of a Panzergrenadier from Germany (mechanised tactic special ability), this unit can board on movement phase and then dismount at the end of movement phase. But again it has to be on movement phase. If any unit is mounted on transport during assault phase they will be stuck on that transport until next rounds movement phase.
Bravery enforcement is a pretty ruthless tactic. I interpret it exactly the same way as you mentioned that the soldiers get scared sh!t and out of fear of dying by there own command fight real hard. They are removed immediately and can not make attacks. Keep in mind that the Commisar can also off himself to give bravery to his remaiing comrades. Commander abilities also apply to themselves.