Do JWs have to report to the Society how many magazines they gave out and who took them etc. ?

Answer 1

No.

The Christian Congregation of Jehovah's Witnesses does NOT actually require individual Witnesses to report their ministry each month, although they do encourage such reports (which typically include simple monthly totals of hours, return visits, and magazines). The Scriptural pattern is actually quite easy to demonstrate:

(Mark 6:7,11,12,30) [Jesus] summoned the twelve, and he initiated sending them out two by two... [Jesus said] wherever a place will not receive you nor hear you, on going out from there shake off the dirt that is beneath your feet for a witness to them.” So they set out and preached in order that people might repent... And the apostles gathered together before Jesus and reported to him all the things they had done

(Luke 9:1,2,10) [Jesus] called the twelve together... And so he sent them forth to preach the kingdom of God... And when the apostles returned they recounted to him what things they had done.

Learn more:
http://watchtower.org/e/rq/index.htm?article=article_14.htm
http://watchtower.org/e/dg/index.htm?article=article_11.htm
http://watchtower.org/e/lmn/index.htm?article=article_01.htm
http://watchtower.org/e/ti/index.htm?article=article_09.htm

Answer 2

They have to report how many mags they gave out, not to whom, and how many hours of door to door service they put in as well as how many hours of bible study and return visits - meaning who they returned to see to follow up after they left mags - so don't take the mags "to get them to go away" because you are just "showing interest" and they will be more likely to return. Trust me - they don't care if you take them or not - they're just doing what they were told to do.

Answer 3

Maybe to track down how many interested in their organisation teaching.