Did they have sex before they were married?

I don't believe so. He spent enough time trying to discourage Jeannie (until at least the fourth season) so I doubt he'd allow an incident that would encourage her.

No, definitely not. The studio would never have allowed for that way of thinking anyway. The producer/writer was given a list of orders and one was that on NO occasion could Jeannie go into his bedroom and Tony was not allowed into her bottle. That was when she was supposed to be on Laugh In and there was a lot of hoo-ha about her showing her belly button. The studio went ape over her NEVER to show her belly button with this other list of demands. Back in the 60's they were very prudish, and it was the early days of TV and censorship was at an all time high.

The episode you mentioned when Dr Bellows is an unwanted guest and Jeannie's smoke goes under Tony's door is an example of it. Note the smoke went under the door and he yellowed out "fire fire" straight away and Tony came out straight away. There was no way the audience could deduce any hanky panky going on, unless of course he had stayed in his room, leaving the audience to that impression.

There was one early episode where she is on board that yacht, and at the very end scene she smokes him into her bottle when he says "Where do you want me to take you Jeannie?" That was before Sydney Sheldon was ordered to never have him in her bottle. The studio relaxed those orders eventually and by the last series, he was allowed into her bottle.

It's been a long time since I've seen it, but didn't Jeannie sneak into Tony's room at the end of the pilot episode after he told her to sleep in the bottle?