I've kept 3 different species of clam, with varying degrees of success. The sad thing is, they can live for months in a state of semi starvation before they actually die, so you may think they're ok when they aren't.
There's only a couple of ways to tell if they are doing ok. One is to weigh them. Weigh when you get them, then about once a month or so. You need a scale that reads in grams or smaller increments. Or you can try to measure them carefully, always being sure to measure the same spot each time. If they are gaining in girth, that's good. If they are gaining weight, that's good. If they are not growing or gaining weight, they are not getting enough food.
They need quite small food items, smaller than filter shrimp do. Single cell algaes are one good food for them, if you're willing to culture it for them. It's not hard to do. Golden Pearls in the 5-50 micron size are very good too, and also good for other filter feeders like fan shrimp. Powdered spirulina is another good food, you need to mix it with water first though. Two Little Fishies make two foods, not cheap, that are also good. Spray dried algaes and Spray dried Crustaceans. I mix them with water first too. I find target feeding doesn't work all that well for clams. To do it properly you have to turn off the water circulation entirely.
So I just pour their food in and I find it helps if you have a circulation pump in addition to the filter. When you feed these very fine foods, turn off the filter for an hour or so, and leave the pump running, to circulate the foods and give the filter feeders a chance to get them before the filter removes them. I got a tap switch, a plug with a switch on it, that allows me to turn the filter off without actually unplugging the thing, much less trouble that way.
Healthy clams usually dig in and bury themselves, leaving only the feeding and breathing tube showing, which are hard to see, since they usually stick up barely an eighth of inch beyond the shell. Sometimes you may see the shoulder of the shell. They usually don't move around a whole lot from where you put them. They aren't that good at horizontal moves, just digging. Mine were rarely more than an inch or two from where I put them.
It's true some species have larvae that use fish gills to get around on, but the ones you're likely to see offered for sale to keep in FW tanks are not among them. Usually you see either the Asian clam, aka Golden clam, sometimes a black and white clam that's rounder in shape. I've also seen some called Shark Tooth, which look like an ordinary lake clam, but with a sharp 'tooth' on the shell that looks very like a shark's tooth. They're about 3 inches long and need a fairly deep substrate to dig into, at least 3 inches of it, and they often leave the tooth sticking up. Mine were, I think, beyond saving when I got them. Only one managed to dig in and I think it exhausted itself doing so. I had 6 and none lived more than a few weeks, poor things.
I suspect Shark tooth and possibly also the black and white ones need cooler temperatures than the Asian ones do, but it's just a hunch I have. I had 3 of the black and white ones, two of which lived about a year, and the 3rd lived about two years. They were gaining weight, albeit very slowly, and I do think they'd have done better in cooler water. As it was, the tank was not heated, it had temperate and cool water fish species in it that didn't need a heater.
I have a pair of Golden Asian clams now, and the gentleman I got them from, who has a wealth of experience life long in the aquarium trade in Asia, told me that one clam needs a minimum of 5 G of tank to have a hope of survival, if there are no other filter feeders in the tank. If there are, they either need a lot of extra food or a lot more tank space to support them. They are not suited for a new tank either. A tank should be at least six months up and running with fish and other critters before you add clams, to allow a reasonable growth of the micro organisms they feed on to establish.
When they die, usually there isn't too much of a problem unless you don't have any scavengers in your tank. If you have snails, or shrimp, they'll find a dead clam quite fast and consume it before it fouls the water. MTS snails are particularly good that way, since they dig all the time anyway. When clams die, the shells pop open and since they are not very far down in the substrate, snails have no problem getting to them and shrimp will get to them too. I've never had a tank foul because of a dead clam, though none of mine were particularly large.
At least one of the species that is sold as the Golden or Asian clam can get to five or six inches but it takes quite a long time for them to grow that big and if they do, you need to provide a deep enough substrate so they can bury themselves.