In American English, "might" is used as a request only if the person being asked to perform the request has already volunteered.
I know you're very busy. Is there anything I can do to help?
-- You might post these letters for me, if you're going to be near the post office.
With regard to your second question about them/those: there is no requirement to change them to those. The following are all idiomatic:
Why are you holding perfumed letters addressed to Mary's boyfriend?
--Oh, Mary is busy, and has asked me to mail them.
--Oh, Mary is busy, and has asked me to mail these.
--Oh, Mary is busy, and has asked me to mail those.
Why were you holding perfumed letters addressed to Mary's boyfriend?
--Oh, Mary was busy, and asked me to mail them.
--Oh, Mary was busy, and asked me to mail those.