You can theoretically take it as far as you could ever want, but after 4-5 generations it just gets bulky. Also, there will be a Little -s- between every pair of parents. If you have to count many generations back, it's generally easier to split up the word into pairs, e.g. "farmors farfars morfars mormor".

farfarsfar, iirc.

It always means paternal grandfather.

"My grandfather is my dad's father" is accepted.

Also "My grandpa is my father's father." is accepted.

Yes, for some reason it only accepts "dad's" and "dad" instead of "father's" and "father", respectively. It is simply a mistake, as both are supposed to be correct.