I want to know if I delete my own question will affect the reputation system or trigger any question asking ban?
I am asking this before deleting because I have already been banned on other StackExchange website and don't want to be blocked here.
I delete my own question will affect the reputation system
Deleting a post schedules a reputation recalc to correct the reputation. So if your post had a positive score, you'll lose the rep and a negatively scored post will restore the rep.
delete my own question will trigger any question asking ban?
Deleting a question doesn't trigger the question ban, neither does it absolve you from the ban.
Quoting the FAQ
An automatic filter is in place to ban questions and/or answers from IP addresses or accounts with a history of extremely poor posts. To avoid bypassing the filter its internal rules are a secret, but it is partly based on downvotes cast by other members of the communities.
Are deleted posts taken into account too?
Yes, deleted questions (if less than 30 days old) and deleted answers count towards an automatic ban.
So a poor post followed by deletion doesn't make the system ignore your previous post. If you don't want to be banned, you should think about what you write and write clearly.
Consequently, deleting a question doesn't trigger the ban either.