Why is it 저희 and not 저의?
저희 is the honorific version of 우리. 저의 means my
why is it 할아버지 and not 할아버님?
할아버지 is means grandfather. 할아버님 is Korean honorifics of 할아버지. You can use either of them
The correct answer suggestion shows me "저희 할아버지께서는 댁에 계십니다." why is there 는 after 께서?
IWhat's the difference between 집 and 댁? Is one a Native Korean word and the other a Sino-Korean one?
they both mean house, 댁 is honorific
댁 is the honorific form of 집. Both mean house
What does 계세요 mean? Like 있어요 but honorific?
Correct. 계시다 is an honorific form of 있다.
What does 댁에 mean?
Honorfic of 집에
At the house/ at home