That screen is just asking to be rotated for vertical shmups...
Not an easy question to answer. "It depends". Ideally, keep your ship in your lower peripherals and focus in a wide cone in front of it. When you move, look at the path you intend to move your ship through. Knowing where ships are coming from helps you manipulate the pattern. If you know where patterns are coming from, you can more-or-less "ignore" them and focus your eyes on other things.
In spite of what the flurry of bullets might make you feel, you shouldn't be reaction-dodging in bullet hell games. It's a big distraction game intended to make you lose your nerve and crash into something.
Yeah, from the mid-90s onward a lot of shmups began giving the player smaller and smaller hitboxes.
For DoDonPachi in particular:
Yeah, everything is avoidable in DoDonPachi. When a difficult pattern is coming your way, try to tap into a safe spot and let the pattern "fall" past you. Often, you'll crash into bullets when you should've stayed still. Try it. Stay still and watch how closely the bullets graze by you.
Depends on the game, but the general rule is that stuff on the ground = safe and stuff in the sky = you can collide with it.
Plenty out there. I'd poke around some "Top x MAME shmups" lists to see what catches your eye. Some favorites of mine that should run smoothly on a RetroPi:
Blazing Star
ESP Ra.de
Dangun Feveron
Shienryu
Batsugun
Giga Wing
Dogyuun
Gunbird
Strikers 1945 II
Armed Police Batrider
Dimahoo