How to be a stern father?

Your father's father is your grand father and your grandfather's father is your great grandfather.

Can't happen unless there's some step-relationship here, such as a man marrying his step-mother, the wife of his father. That still makes you your father's son in any case, but now you have become...

Whether "your father and I" or "your father and me" is the correct construction depends entirely on how it is used in the sentence. "Your father and I" would be correct only where the use of "I"...

I would think that would make him your great grandpa!

My father's house. The apostrophe shows that your father is in possession of the house.