Fans are generated at random.
Fans won't be family members
Fans have the options to interact by asking for an autograph, hug, take picture with, take picture of, attempt introduction and limited chat options
If your Sim interacts with Fans by giving hugs there's a high chance they'll develop the no touching quirk. Celebrities, based on level, with have up to 4 quirks based on interaction with Fans or with food types, etc
The quirk no touching will cause your Sim to decline random fan hugs but can also effect more personal relationships.
You can't stop Fans from asking for hugs or trying to hug unless they have the no touching quirk, in which case they'll decline being touched.
Edit- fans who are generated at random won't always be the same. I had a Stan quirk which is a super fan and they'll show up at your house. My Stan was rarely the same to include mortimer goth as well as random npcs. So the trait or interaction of npc fans can change or go away or return. It's really more like it's just assigned to whoever is spawning in at random.