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.