In answer to your question of how to say 'grandmother' and 'grandfather' in Farsi, it is quite helpful that i am Persian myself, therefore I speak Farsi!
First of all, the way to say Grandmother is generally 'Maman Bozorg' (written in English letters, since we use farsi letters)
'Maman' means 'mother' and 'Bozorg' means big. So it literally translates to big mother.
The way to say 'Grandfather' is 'Baba Bozorg'. Again, 'Baba' is 'father' and 'Bozorg' once again is 'big.' (Big father).
However, generally in our culture, we do not refer to our grandparents in these terms. The most common way that I have personally heard people address their grandparents (particularly young children) is 'Mamani' (grandma) and 'Babayi' (grandpa). This also depends on the way the child's parents teach the child to address their grandparents. I've personally heard the term 'mamani' more than anything else.
It is generally respectful to add 'joon' to the end of an elder person's name. Therefore, it is not uncommon to refer to your grandparents as "(name) Joon." For eg, my grandmother's name is Roya, and we were raised to call her Roya Joon, which is what we still call her. So that, too, is an option.
I hope this helps!