Edited to add: also... will the larger snails we're planning on getting (3 zebra nerite and 3 mystery) eat these little guys?
No. Assasin snails are (so far as I am aware) the only snail that will eat the smaller snails. But not being all that up on snails, there may be others but I have not seen them mentioned here.
But you're saying if I don't overfeed then the numbers shouldn't get too crazy? I guess I just had it in my head that large amounts of them were bad as I've seen some people complaining about them getting out of hand. If anything in my opinion they'll add even more interest to the tank on top of keeping it cleaner so I won't worry about it. Maybe if that's the only one I'll add a few more so they can breed. Or are they asexual/capable of breeding on their own?
You might be surprised at just how much organic food there is in an aquarium. I certainly do not overfeed my fish, and I have hundreds of Malaysian Livebearing Snails and some bladder/pond snails in each of my tanks. Rarely do they get very large before they die, and I suspect this may have something to do with the lack of food. But I know that they are there at the level they are solely because there is sufficient food to sustain them. And if they were not there, that natural organic food would be polluting the water. Snails and good bacteria exist in natural ecosystems for a very good reason, they help the system. If they are "bad" because of their numbers, that means you have a real problem causing this, so once again, the snails are not bad, but your maintenance might be.
According to Bob Fenner, most snails are hermaphroditic, both male and female. Cross fertilization is the rule, though many small species are known to self-fertilize.