Does the StackExchange system still count questions that I've deleted toward my potential of being blocked?
I won't describe the exact criteria the automatic question ban uses, but I will say we hope people will edit their poorly-recieved questions rather than delete them. We allow askers to delete their questions for the hopefully rare cases when people discover shortly after they posted that the question is inappropriate for the site and can't be recovered. For instance, people sometimes accidently post on the wrong site or learn via comments that they misunderstood the site's topic space. If that happens now and then, the automatic ban won't kick in.
People who use the site responsibly are, in fact, unlikely to be blocked from asking. We want to block truly abusive behavior, not punish people for the occasional slip up. There are warning notices when you get close to being blocked. Those notices should be taken seriously. If at all possible, consider going back to improve old questions with edits. It's also the time to think twice about posting marginal new questions.