I've pulled a new 12 gauge/20 amp circuit to an old bathroom that is
currently using 14 gauge with no ground wire. I need to add a fan and
another light.

Is this correct:

I can use this one 20 amp circuit for everything inside this one
bathroom (one outlet, 2 lights, one fan) as long as nothing else is on
that circuit.

The outlet near the sink must be GFCI of course. I will run the feed
from the breaker to this outlet, and then I can make the other
fixtures (lights, fan) downstream from this one GFCI outlet. This
makes everything in the bathroom GFCI.

Thanks !