Bullpup fan here.
You can fire a BP with your left hand around a barricade, but you can't get into a traditional cheek weld position. So it is only good out to a limited range, but you can still put rounds on target. Hold PG in left hand, mount on shoulder, angle away from body, right hand grasps magazine or mag housing.
Even then, it is pretty rare for people to switch shoulders with their regular long guns. Most people haven't trained for it, don't do it as well, and just contort themselves around their cover to return fire with their right shoulder. Also if somebody is using a tac sling, this will often make it impossible to shoot from your left shoulder anyway without undoing the sling.
Trigger pull is entirely up to the design. You won't ever have a crisp target trigger, but you can get a trigger that is equal to most military rifles. The Tavor I tried had a decent trigger pull.
The FN 2000 does eject forward. One of the Russian guns that competed in the Abakan project also had forward ejection, and that was over 10 years ago. (basically the shell is lifted during extraction, and then shoved out the front when the bolt returns)