Can I share arcade only with family?

See What types of content can I share with my family? - Apple Support. I think if you have a Family Share and one person in the family subscribes to a service that is shareable then everyone gets access to it. See also What is Family Sharing? - Apple Support and the section Everyone's personal files and preferences remain private.

tt2

Not really no, in particular the family organizer cannot avoid being ultimately responsible for purchases by other members of the family.

tt2