I have a household where they fight over whose turn it is to go steal the gnome back. Sometimes more than one will head out, and sometimes they'll head out more than once in the same night. I think the highest number of gnomes I ever had "stolen back" was four in one night. (The family only ever has one gnome placed, and therefore stolen, at any one time.)

the gnome is part of the community lot Buy Mode catalog.

stolen gnomes; is the thief always someone that lives on another lot?
and would the stolen gnome appear somewhere on the thief's lot (after saving and exiting the victim's lot and entering the thief's)?

The gnome is also part of the residential Buy Mode catalog. Lots of things are enabled for both catalogs (like chairs, tables, flamingo sculptures...), but they aren't different versions of the same thing. They're just the same thing, period.

The thief is always someone who does not live on the lot where the gnome is. They are not always playable sims with a lot you can visit. Townies can steal gnomes as well.

The gnome does not appear on the thief's lot or in the thief's inventory to the best of my knowledge.

You cannot direct a sim to go steal back a gnome. They will do so autonomously, usually around 10 pm, and only if they have very low Nice points. Most of my sims who go to steal the gnome back have 0 or 1 Nice points, but my sims tend to be extreme: they either have 0-1 Nice points, or they have 8-10. I don't know if sims with 2-7 Nice points will steal back a gnome or not, or where the dividing line is.

I will kindly point out again that Opal, my 10 point nice sim did steal back a gnome, so they can even if they don't normally. I think the game looks for a mean sim but if none are there it will use a super nice sim.

another question

how can interactions (object, social) be changed between autonomous/player-directed/both?

Depends on the interaction. Many can't be changed. Some can be made to happen with cheats. Some you might be able to find a mod or create one if you are a programmer/know your way around SimPE. (I'm guessing you don't?) What specifically do you want to change?

Myone Sim came back from work with 2 gnomes in her inventory recently! No idea where she stole them, but she must have

Is there a reason why you can't use the stupid questions faq like everyone else is supposed to?