Is it okay that instead of pulling my finger away from the fret board to avoid hitting other strings i just pull my finger straight on to the string below to mute it, or will this get in the way in the future? I'm on a acoustic and i've only ever played with my fingers, so I'm trying find a way to have speed with my left hand.

Maybe this is normal practice. i don't know.
That can definitely get in the way. What if you are playing the string below it at the same time? For example, something like this:

Quote by Geldin
Junior's usually at least a little terse, but he knows his stuff. I've always read his posts in a grouchy grandfather voice, a grouchy grandfather with a huge stiffy for alternate picking.
Besides that, he's right this time. As usual.