No, anaerobes do not require oxygen to survive, for they do not carry out cellular respiration with oxygen as the final electron acceptor. Rather, they typically carry out either fermentation or...
If they CAN survive without oxygen, they are called facultative anaerobes. In other words, these can survive with or without oxygen. If they CAN ONLY survive if there is no oxygen, they are callled...
Not very long, it depends how long you can hold your breath for. As if you were in a pool and you were having a "how long can you stay underwater for" contest.