If you take a screenshot from a game, add a word balloon and upload it, then no, that is not allowed.
If you draw the exact same thing (take a screenshot, draw what it looks like by hand [note that there is a big difference between drawing and tracing] so that it is your own work but based on something else) then that is perfectly fine. For example, this strip
in Ctrl+Alt+Del is entirely based
on America's Army, but it is not footage from within the game, it was drawn.
I sent in a scanned image and it hasn't been edited yet. It looks pretty crappy.
How it looks is irrelevant, the committee does not judge your skill, they just want to make sure you are a human and that it is your own work. So long as the image was inside the requirements (less than 500Kb and not super-huge, like 1200x1200 pixels) then you shouldn't get rejected for that. If the image was
outside the requirements, then you might be asked to make a new submission.
...Am I alowed to draw backgrounds...
So long as you draw them, then yes. Not if you copy them,
...what else should I take into consideration?
There are like ten billion webcomics about video games. Try and make yours original. If it is not original, try and make it look good. If you can't make it look good, then try and be funny. If you can't be funny, then at least try and be different to the other ten billion video game webcomics. And remember why you are doing it. If it is for the fun of it, then you can pretty much ignore almost everything that anyone else tells you. So long as you are having fun (and you aren't copying) then go right ahead.
If you are doing it to make money, don't quit your day job.