No one really has defined exactly how many deletions it takes, but if you delete too many questions or answers, this is the potential consequence: What can I do when getting "We are no longer accepting questions/answers from this account"?
In short, there is an automatic process that analyzes a number of criteria, one of which is the number of deletions and the result is you can be banned from asking more questions/answers until you raise you reputation enough to lift the ban.
But in response to your edit, a deletion will adjust your reputation accordingly (a negative score post will add the lost rep back, and a positive score post will removed the gained rep). As such, a zero score post will not affect your score at all. But regardless the potential for suspension or automatic ban is still there if you do it too much.
And for your second edit, my understanding is the question/answer ban will affect anyone, although for an established user with lots of rep and numerous questions/answers, due to the other criteria that is considered, it would take a significant amount of deletion to kick in (can't find a link to support this though).
And just to add some addition info, and a really great answer to a similar question, take a look at this answer to the question FallenAngel linked in the comments. I think that pretty much covers what I said and more.