1. Yes, God is a third person pronoun.
2. "My God bless you" is wrong. "My God blesses you" is correct. However, it is uncommon to attach a possessive pronoun to God so people usually just say "God", not "My God". "My God" gives the impression that you are intentionally highlighting that the God in your religion is not the same God in the other person's religion.
You may have been referring to the phrase "May God bless you." Here, "bless" is in the infinitive form (to bless) instead of the simple present form for third person pronouns (i.e. blesses) because of the use of the modal verb "may". However, it is common to hear people say "God bless you" or "God bless". Although they are grammatically wrong if taken just the way they are, they're actually just a shortened version of "May God bless you" and so they are generally accepted as correct.
3. Yestreen is an extremely old word that means "yesterday evening" or "last night". To my understanding, it was commonly used in poems or by the Scottish people in the past, but is not commonly used anymore now.