Questions can only be removed by the moderators, if they are found to be in violation of the Community Guidelines. If they're not breaking any rules, then questions are open and answerable indefinitely. That's one of the reasons why it is so important to think about what you post online, as once it's out there, it's almost impossible to take back. If you'd like to know more, there's a Help Center article on the topic:
You can't delete a posted question or answer or comment you done. Only the moderators are able to do that. But for your recent questions and answers you can edit them if you want through 15 mins only from posting them.