ok in order...
Yeah the keyboard layout is a bit awkward... for space based parts i find myself using the mouse to control the ship, then space bar for phasers and assigned numbers for torpedoes (right click and drag them to assign to set numbers)
that way you can stick to mainly mouse orientated work for space, and the standard WASD for ground based shooty parts...
Single player or multi-coop... i've done the entire game pretty much single player, with a few missions with some people when i needed the extra help... i wouldn't say it's necessary for all of it, but on and off, it's more fun
Different ship types from character class are fine... i've got a science officer manning a tactical craft, i normally play tactical character and use the cruiser class... doesn't make any difference from what i can see...
Hope you're having fun though
M