I'm wondering how long typically the private beta period will last? I could not find info on the cs.SE/FAQ (or maybe I missed it).
Private betas are evaluated after 7 days. Most become public betas at that point. Sometimes, a private beta that hasn't had enough traffic or that's perceived as low quality might be told to shape up and given an extra period of time to improve.
I must say I'm a bit concerned that our beta is too slow. While there aren't any hard-and-fast rules, we only have 60 questions after 5 days. Even French, where traffic later dwindled to a trickle, had 125 questions in its 7-day private beta. 16 unanswered questions is another concern; many of these are difficult questions, but it does mean we really need to work on recruiting experts on a broad range of fields.