Sometimes I try to have good manners out in public and when I need to burp, I make an effort to do so with my mouth shut. When this happens, I can re-taste and smell the food I just ate. Can other people smell this odor if my lips are sealed?
Yes. The smell still comes out your nose.
Don't be silly, OP. The air is trapped in your mouth. Once you open your mouth, though, the air that has been fermenting will fill the room.
Oh, just let 'er rip.
Yes, I've smelt the nimbus of sausage and Omega 3 fish oil from otherwise courteous burpers.
Also, if I fart, but inhale really quickly to vacuum up the fumes, will it prevent the odor from spreading?