I am new to using vim. So I think my questions will be in the beginners level only. Should I wait till public beta to ask my questions? Will asking beginner level question impede the site from being launched?
"beginner-level" is not a particularly useful classification here. The criteria you should apply, especially during the private beta, is:
"Does this question require an expert to answer?"
How do you, as a beginner, know whether your question meets that requirement? Simple: do your research!
Have you read a "getting started" guide for your editor of choice? If you haven't spent 10 minutes doing that, don't expect someone with years of experience to put much thought into answering your question.
Have you searched for the answer first? It's ok if you did and simply weren't able to find an answer you could understand - but use that experience to explain the sort of assistance you require.
Plenty of experts enjoy answering "beginner" questions, but few enjoy answering questions that are unclear or have already been answered - and answered well - dozens of times before. In particular, this site currently sits in the shadow of an extensive library of high-quality questions and answers - slavishly recreating them without adding anything new and useful isn't a reputation y'all want to be cultivating, particularly during the private beta.
I think beginner questions are fine. I think this site should aim to be the goto site for anyone with questions about Vi/Vim, and as such it should contain answers to any and all (on-topic) questions that someone might ask about Vi/Vim, and not only the questions for which answers cannot already be found elsewhere on the web.