Welcome! To answer your questions...

Yes, you will need an account for each character you want to run simultaneously with another.

No, you don't need more than one screen to do it. I currently run 1 character on one screen and 4 on another but some have 1 screen for each character or just one for all 5 (or however many they run) It's all based on what you prefer.

And yes, you can use more than one computer but depending on the specs of yours, you may or may not have too.

The program is KeyClone. Search here. There's a ton of information on it. Or..you can use Octopus. It's somewhere on here too. With KeyClone you have to pay for the software but you get amazing support. I've read Octopus is great too and it's free. With whichever one you choose, you can't lose.

Class ideas...I've never run two melee classes. I've heard they are complicated but hey, to each their own. Try it out and if it doesn't work out, you can always roll another pair. Good luck!