It's a generalised typeclass for wrappers. It's not called "then" but "bind" and spelled (>>=), which doesn't exactly evoke useful associations for newcomers.

It is what you described at high level. The devils are in the detail. People keep using words to describe the detail when code shows everything.

Because the interface has a few complicated rules associated with it. If you break them, the compiler may accept your code but it won't work with a lot of libraries that are supposed to work with any monad.