Is it okay to use in a small space, like an rv. Where people would constantly be around it, with windows closed, and hvac on most the time?

I have Ona in my kitchen where the lid is on most of the time and taken off as needed for odor remover. I add a little water from time to time and I'm still using the only jar I bought and it has lasted for years .

Does this work on body odor? A coworker who has such strong body odor that I have to hold my breath when I open my office door...

It will displace/distract most odors, and yes it would work on the characteristically sulfurous smell of body odor. Just realize that if you use Ona in an office, you and everyone else will then be smelling the Ona constantly. If the co-worker's body odor is really that noxious, then we suppose this would be one way to deal with it. Have you considered leaving an anonymous note for the co-worker informing him or her of the problem?

Will it take odors out of fabric?

Will keep clothes from taking up smells in same room. Will not remove smells from already worn or dirtied fabric; it will keep smell from dirty fabric out of the air in same room.

Where in the house is the best place to place it?

That is a small container and works best in a small space. In my experience, It doesn't last too long. I buy the gallon jug and have the breeze fan and keep it in my living room/dining room. It freshens the whole house in days. Then I unplug it and cover it up or else it dries up fast. It's too expensive to waste.