1. Press CTRL-Amiga-Amiga (Amiga keys are the A keys on either side of the spacebar)
2. Yes. But, to use HD floppies (as HD) you'll need a HD floppy drive. The A600 shipped with a DD drive.
3. Not directly. But, you can get an external scan doubler/flicker fixer that will allow you to connect to SVGA monitors. However, they're hard to find and expensive. You can however get S-Video by using a converter (also hard to find, but not as expensive). Either is better than the standard composite.
4. Yes, but I think all that is available now is DIY stuff. (ex.
http://www.aminet.net/package.php?package=hard/hack/PCGamepad2Ami.lha)