Forgiving someone doesn't mean you're obligated to subject yourself to their problematic behavior.

I agree. Forgiveness is more for my peace of mind.
Also, I can forgive you but it doesn't mean I will let you enter my circle again.

The word forgive is actually pretty ambiguous.
For some it means no longer seeking revenge for a foul deed.
For others it means giving the other the benefit of the doubt but still not trusting them.
For others yet it means feeling empathy for the one that harmed us.

Yup

Right

It also doesn't mean that you forget what they did or not take their past actions into consideration when dealing with them in the future.

Correct.