Maybe you forgot the veb in the sentence : My friend wears glasses and always ___ CARRYING a bag. In this case it is 'is' because 'My friend' ,the pronoun is 'he' , and it is always 'he IS'. However 'carries' in the present tense is the correct one to use as Tony mentioned.

None of them make sense.

Or, it could be: "always carries a bag"

None of the above make sense in that sentence. It could be "My friend wears glasses and always HAS a bag."