What is your favorite and most useful question to ask?
Do you like to ask more open ended questions or specific questions?
About how long will you talk (or chat) with them?
It really depends how long I talk to each person, some people you can tell pretty early on are going to be very helpful and I try my best to get them to talk to me as long as I can. One thing I always try to do is record those conversations, with permission, in order to come back to later and take better notes on what was said.
Watching people use your app can be illuminating too but it can also be a bit misleading because people won't always act/interact with your site/app the way they normally would because they are being watched.
Good luck with customer development, it's fun/rewarding/daunting.
If you are still early on, I would start with "What do you use currently to ________?" Where the blank is the problem you're trying to solve better than it is currently being solved.