I know that on SIMLOGICAL you can find PRISON SET for working jail/prison. But (since I have never tried it) is it OWNABLE BUSINESS only? Can it work on unowned community lots? Is there (on some other site) a similar PRISON/JAIL SET system?

You can use the simlogical set on ownable businesses and regular residential lots. In fact, I think most people use it on a residential lot where they have a sim or sims acting as police & jailers.

I haven't seen another prison set around, especially since you can move other sims in with mods to get them on the lot. The main thing is making sure sims don't show up elsewhere in the neighborhood when they're supposed to be in prison--Inge's prisoner tag + the visitor controller helps with that.

If you're unsure about it, check out the tips at the bottom of the prison set download page here as well as a few threads I found on MTS:
Do you use a prison system in your neighborhood?
How you guys implement prisons on your game?
And Running Institutions (i.e Schools) on Residential Lots might be helpful for general tips on running institutions and lots where you need to manage a bunch of sims.

Defo wouldn't work on community lots. I've tried to run one on a residential lot but to be honest it was a lot of work and required a lot of sims. I kept some of the cosmetic parts and mock up my own prisons now if I want one, not using the mod.