FW Nerites are good for really small tanks. They're tiny, don't breed in fw except with a lot of deliberate care for it, and frequently kept as snails in shrimp tanks. All Nerites require high KH and pH though and you have to be a bit cautious with species since sometimes there are more strictly brackish to saltwater species sold in fw and they will jump ship and risk dying repeatedly until you put them in the right water. I've kept Theodoxus species in tiny tanks with shrimp in the 1gal range (might have been more like 1.5; I don't recall eactly as it was many years ago, but it was a quite small desktop tank with java fern and minimal water flow). I've kept Theodoxus by themselves in 0.5gal.
Absolutely not true. Many species don't reproduce in smaller aquariums without a lot of special care. Some can't reproduce in normal aquariums at all.
EDIT: will add even some "pest" species won't explode in population if the conditions are off from what they need. Some Planorbis are actually pretty finicky to maintain. The main culprits for population booms are Physa, Helisoma anceps, and MTS when there is serious detritus issue (otherwise they can often exist in the substrate totally unnotcied and you never have to worry about them if the food is in balance)