1) You can define new functions (and values, and types, type classes, instances, etc). You can "redefine" these things only insofar as you can shadow them.
2) I'm not sure whether they mean the ability to persist your state to disk and restore it (which GHCi lacks), the ability to refer to previous results (in GHCi, the previous result is called `it`), or just the ability to bind variables (of course you can do this in GHCi).
3) Usually "Show" instances are meant to be embeddable in code. Sometimes they need a little massaging. Sometimes they're just broken, from this POV. Sometimes they're just broken, period. But it holds for a lot of values.
4) You can run GHCi in the context of your project (see cabal repl and stack repl commands).
5) GHCi very much fails at this - no way to add anything to a module, so far as I'm aware.
6) GHCi more-or-less lacks this kind of functionality. You could run your server's "main" function from the REPL, but there's not much you can do to it.
7) :reload
8) There's an increasing amount of such tooling; only some of it has any particular tie to the REPL, per se.
