Common Bladder or a Pond Snail for sure hard to tell which one from the angle, betting on the bladder though. Does it have donkey ears or antenna? Donkey ears = Pond / antenna = Bladder
So to answer your questions
Plants - Will not harm
1000+ Babies - Oh yea you'll have babies....:grinyes:
Just keep your feedings light and they should not become a real problem if they do there are a few means to get rid of them.
#1 Manual Removal
#2 Assassin Snails
#3 Snail eating fish but only if you are prepared to keep them.