why is it 'me' instead of 'mij'
"Mij" puts emphasis on the fact that it is to you that he is bringing the magazines. "Me" does not.
dank je wel!
Both should be accepted (unless it's an audio exercise).
Tijdschriven: time writing?
There is tijdschrijven, but that means accounting for worked hours (writing down time). The tijd in tijdschrift refers to it being a periodical