sentences with '' and,being.....''

Both sentences mean the same thing. As used, I would say that "being" and "which are" mean the same thing (something exists), so the second sentence contains a redundancy.

Your first sentence may be acceptable grammatically, but it looks rather clumsy. I would say

The veins composing the plexus are thin walled and, having no valves, may pass blood in either direction.

Your second sentence is not acceptable, which cannot follow and, in such a structure. Plus are being is not appropriate here, as this property does not only apply to the moment of speech. If you really want to rephrase the initial sentence, which is clear and correct as it is, you could say:

The veins composing the plexus are thin walled and, because/as/since they have no valves, may pass blood in either direction.