Is there a difference between 집 and 댁?
Yes, the latter is the formal version of the former. Here a list of such words.
How come I can't click this link on mobile...
댁 is the honorific form, so you would use with honorific subjects such as older people/ people of respect.
Is 계세요 like the honorific version of 있어요?
I know 우리 could also mean "my" and not "our", but "our" should still be accepted. also it marks "house" as wrong and insists it to be "home", although there shouldn't be a difference, as there wasn't in previous times.
"My grandfather is home" should really be accepted.
I also think "our grandfather" should be accepted. Without context, it is unclear if it means "my" or "our".
If I'm speaking to someone who is not my sibling or cousin would I still say "our grandfather?"
Yes. If you really want to emphasize "our" and not just "my", you can also say 우리들의
I put, "Our grandfather stays at the house." Did I get it wrong because it was not 우리들의?
I thought 우리 translated to 'our' rather than 'my'?
It's confusing but when speaking formally it can mean my.
Our should be allowed seeing as how other questions allow it.