1) Not really necessary, but a lot of people like them. The extra buttons on gaming mice, especially, can be kind of nice. With the typical use, your right hand isn't doing much besides movement, so moving some hotkey functions to that hand can make a noticeable difference.

2) Right hand on the mouse at all times. Unbind left/right turn from your keyboard, put strafe on AD (or leave them on QE and put skills on AD), and do all your turning with the mouse. Use keys around WASD for skills. 1-6, QERTY, FGH, ZXCVBN (or as far as you can comfortably reach), plus alt/shift/ctrl mods for all of those, gives you a boatload of available keybinds. You've already got the idea of prioritizing your binds; the more often you hit it or the more important it is, the easier the key you put it on. Also put similar skills in the same places across classes as much as you can; stuns in the same place, buffs on the same keys, etc. (Z is always my stun key, 1-6 are defensive buffs on tanks, offensive buffs on DPS, main rotation is FVG, for example).