How long does it take for a question to appear in the reopen queue, after someone cast the first 'reopen' vote on it?
I cannot test this myself, because you cannot see questions you already voted on in the review queue.
There is an automated background job that adds posts to the review queues. This job runs every few minutes, but exactly how often the job runs is not public information. It is in the order of 'a few minutes'.
However, a reopen vote (or even an edit) must have existed for at least 15 minutes before a post becomes eligible to be bumped into the review queue. Once that 15 minutes has passed, it will be added to review the next time the automated process runs.