Yes u can.
I always have the volume at max, and tone control at the flattest position, so I'm going to install a bypass switch just to see if it gets any better, tho I doubt I'll hear a difference.
I figure let the geetar supply the tones, and the amp can do the tweaking.
Yes, you can do that. The tone control can be removed, and the volume control is there so you don't have to walk back to the amp and reach over to it during a sond if you want to change the volume. But it doesn't have to be there.
Do you know if it's an active pickup or not? If the pickup is passive it doesn't make a difference, unless your trying to blend two pickups.
For more info see: www.guitarelectronics.com, you can find loads of wiring diagrams there.