a)Yes, units hit do get to fire back. b) The rule book is not clear on this point. However, I would say that yes you can still bombard. While I can see an argument going the other way based on a certain interpretation of unclear rules, logically its likely that a battleship would not wait to bombard the shore until after the landing troops had been fired upon.
You can still bombard. Battleship bombardment is dependent upon the number of units that offloaded from transports, not how many of them actually made it ashore.