I'm working on a 2D side-scrolling ship control game similar to Gradius III for SNES. (Is there a better term for this genre?) Here's a sample, with the action starting around 0:30.

These are my trouble spots:

1: I want to control my ship with either the mouse or keyboard. Initially, I used another's code which made the unit a GUI element, but I forsee problems with various screen resolutions due to the offset. (When the game is windowed, the screen's coordinates usually aren't the window's coordinates.) Thus, how do I get the mouse control to work with a variety of resolutions?

2: I want a ship that can instantly change directions and stop on a dime. I tried disabling gravity on the ship, but that causes the ship to skid. How do I get tight controls in Unity?

3: How do I get selective collision? Since I want this game to be multiplayer, I want to check collision with the sides of the screen and with enemies, but not with other player ships.