By COM you mean RS-232C. You cannot use a straight-through USB connection. You will let the magic smoke out of the USB hardware. You need the cable that requires the driver.
1) You will not normally get a GUI over such a connection. I mean, there are extreme situations where you can, but I wouldn't consider those at this point.
2) Again, technically you might be able to use RS-232C for output and a different keyboard for input. But I wouldn't attempt this.
3) Yes. You can do that; it's precisely what those adaptors are for.
4) This is due to historical standards, and standards not really adhered to. RS-232C shouldn't even be on a DE-9 connector anyway.
