Lots of questions. Finishing a basement with a bathroom, bedroom and a family room.

Are GFI circuit breakers or outlets needed in the basement family room?

Arc fault breakers are required in bedrooms only and are gfi's required in a basement bedroom?

Running a 20amp separate circuit for the bathroom, can you run the main power to the GFI, then to your other outlets (within the bathroom), then to the light switch and fan? And will this make the fan and light gfi protected?

Only outlets in a unfinished basement need to be GFI, once it is finished off to a room, the outlets can be standard .

Yes AFCI protection is for bedrooms only, including lights and the smoke detector. Should check with local code as some states have waived the smoke detector on AFCI and do not require, or allow, it on AFCI.

The bathroom outlet needs a 20 amp circuit, and GFI, the lights in this one bathroom can be on the same outlet circuit, but do not need to be GFI protected. To connect the lights and fan without GFI protection, simply splice onto the feed to the Line side of the GFI outlet. Best to not GFI protect the light at least so you still have lights if the GFI trips.