The FDA calls it “pasteurized processed American cheese food.” In order for a food product to be a true “cheese,” it has to be more than half cheese, which is technically pressed curds of milk. So each Kraft American single contains less than 51% curds, which means it doesn't meet the FDA's standard.
Just cover the pan and pretty much any cheese will do. I use pure cheddar in ours, which sucks at melting, and I can get the grilled cheese completely melty and the bread properly toasted.
Just make sure to eat it before it cools, otherwise it gets chewy.
Depends where you draw the line and the exact product. American cheese is just cheddar cheese, milk, and an emulsifier. The ratio of cheese to milk usually classifies it as "not cheese" but it's still actual cheese and milk. You can make American style cheese with all kinds of different cheeses, too, we just mostly do it with cheddar or a cheddar colby blend
Heat a little bit of milk, throw in a little sodium citrate (I think it's like 1/2 a teaspoon per pound), stir until dissolved, cut or shred a big block of cheese up, melt that in, and you get magic cheese that tastes the same (it takes very little milk to make it work) but melts and remelts without issue. Instead of a bechamel where the oils separate out if you don't mix every 30 seconds to reheat it, you can just nuke the hell out of it in the microwave with no issue.