Asking about an opponent’s double

One of the advantages of BBO is that you can ask about a call at any time. You just click on it and that asks the person who made the call to explain. So the answer to when you can ask is whenever you like. You must remember that not all players are very good at bridge. Looking at the two examples you gave I would think that neither opponent was particularly competent. In the first case I think it is a simple takeout double on a not very suitable hand. In the second case I am quite sure that West just produced a really poor call, possibly having misread the auction or misclicked, and I doubt that asking him the meaning would have got a helpful reply. Your original question was whether you can ask about an opponent’s double. The answer is yes because you can ask for an explanation of any call. If you had been playing face to face then you could have asked whenever it was your turn to call or play.