Red stars in NGC 884

As has been pointed out elsewhere, open clusters are considered to be
relatively young with stars of blue and white. So what's the deal with the
high population of red stars in NGC 884 (one of the clusters in the double
cluster). I've seen red stars in other open clusters, like the bright core
star of M37.

Is there a relationship between red (carbon?) stars and planetary nebulae?
Are all carbon stars potentially remnants of planetary nebulae? If so, maybe
the central star of the planetary nebula in M46, will appear red in the
future, having blown off some of its shell. Sort of a premature aging.

Are all red stars carbon stars?

Curious,
Stephen