Okaay...
Well, the first thing I would recommend is, if you don't already have them, work on developing your verbal filters. This will prevent you saying totally inappropriate things at inappropriate times.
What I mean by this is- for example, when I'm with my friends I tend to curse and make raunchy jokes on a scale that would make a sailor blush. HOWEVER, I've trained my brain such that when I walk into a conversation where that's not appropriate (with my grandmother, with my department chair, in a professional situation, etc) the verbal filter immediately kicks in and those things absolutely do not come out of my mouth under any circumstances.
This takes some practice, but if you've having to sit there and go through a process to mentally censor yourself, you've wasting time and look awkward. It needs to be automatic. And not just with cursing, if that's an issue, but with things like text speak, inappropriate internet references, etc.
Then, I would absolutely get over the 'stupid question' paranoia.
Sure, stupid questions do exist. That's not the point.
What makes a question stupid is not ignorance per se. After all, you're there to learn. They assume you come in ignorant and won't hold it against you as long as you're actively trying to learn. The stupid questions that do get held against people are the ones from somebody who clearly wasn't listening to what was said 5 minutes ago, or who is putting no effort at all into learning something.
If you're there in their office asking interested questions about their subject, even very basic ones, then this is not a mistake you'll be making and should not be sitting there analyzing a question for stupidity in your head. So don't be afraid to ask academic questions, they'll be more than happy to help you learn.
Also, when you're going to office hours, have some questions prepared -either on class material or the subject in general. Ask them. Ask whatever else pops in tangentially along the way. Then when the conversation is winding down and you don't have another question at the moment, say thank you and walk out. Do not sit there and try to come up with something else to ask for the sake of 5 minutes more conversation. Just leave before it gets awkward. Go get coffee before your next class or lunch or whatever, but go while it's still comfortable.
Because if you leave while it's comfortable, then it will be smoother the next time you come back. If you stay till it gets awkward, it will start off awkward the next time and continue to compound the more you do that.
Go for the positive spiral, not the negative one.