Yes, Norns is secretly a small computer running Linux, so you can store samples in folders to be loaded and manipulated by scripts.
Norns doesn’t have just one built-in synth engine. Norns runs SuperCollider, so there are quite a lot of possibilities for synth engines, and more can be reimagined by you or any of us. Concretely, some scripts like Molly the Poly and FM7 offer polysynths that you might check out in terms of what’s already on offer.
Yes-ish. Norns can do USB MIDI out. Norns runs one script at a time, so you’d need a script that sends out MIDI and internal Norns audio at the same time. Off the top of my head the script that is most likely to do that currently is Orca. Of course, the possibility of writing your own script for your own needs is always there!