JOEL - Sounds like you're doing fine to me on this principle. It is completely up to you and your child about paying tithing on monetary gifts. We pay our tithing according to our faithfulness and willingness to sacrifice. If you want to sacrifice a little more, you will be blessed accordingly. Normally we would of course not pay tithing on any gifts or presents that someone has purchased for us. However, a good way for parents to train young children in the concept of paying tithing is to have them pay on gifts of money that they might receive as a birthday present from a grandparent or other relative or friend or perhaps from an allowance we give them. That's what we did with our kids and it did help get them into the good habit of paying tithing as they got older and started working.
I can't tell you what to do; this is your decision to make. As a 1970 statement from the church leaders tells us "every member of the Church is entitled to make his own decision as to what he thinks he owes the Lord and to make payment accordingly" (Mar. 19, 1970; quoted in Doxey, Roy W. Tithing: The Lord's Law. Salt Lake City, 1976).

PRECIOUS - Does the Patriarch have a title name like bishop, president, elder so and so? How do we refer to the Patriarch of our stake? Do we call him Brother _______, or Patriarch _________?

JOEL - Some use the term Patriarch________, but it is best not to use such titles in casual conversation. Patriarch is an office in the Melchizedek priesthood, so the most proper way to address him would be the same way one would address an Apostle or Seventy of the Church; either "Elder" or "brother".