Unless you have a ton of them or you personally don't like them, snails aren't really a problem. If you overfeed the other tank inhabitants they can get out of control, but if you don't, they generally don't.
The snails could have come in with virtually anything you put in there that was previously in a fish tank. I've found blobs of snail eggs floating around in the bag with new fish and snails crawling about on the inside of those bags as well. That said, they almost certainly hitched a ride in with your plant and also almost certainly had nothing to do with its death. Pond snails don't eat live plants. Some species of ramshorn do (Columbian ramshorns maybe, can't recall??)
As far as reproduction goes, snails are a very old and diverse group of animals, and they have a variety of reproductive strategies, ranging from single sex organisms that require sexual reproduction to snails that reproduce parthenogenetically (eggs develop without any fertilization at all.) In the case of many freshwater snails, the animals are hermaphrodites, though as was noted, this does not necessarily mean that they can self-fertilize. In the case of pond snails, however, a single animal is capable both of breeding with another and of self fertilizing.