I don't speak Harlequin, but if the troop master is a unit champion then yes he will suffer morale. If the troop master is a character than he isn't part of the unit and deploys, moves, advances charges etc separately from the unit and so wouldn't suffer morale for the units casualties.
If a weapon is an assault weapon then yes, it can be fired at - 1 to hit after advancing. Rapid Fire, Heavy, Pistols etc cannot. The rules for weapon types are listed in the shooting phase section of the rulebook.
Do you fight for the Dark Gods? The Drukhari gave birth to one of them. By partying.