"Is your grandfather alive?"
Translation:Lever din farfar?
This is a question, so the verb has to go before the subject. The only thing that can go before the verb in a question is a question word (such as when or who) or a phrase that has the same function as a question word.
So you put the verb first. The subject is din farfar – the order between those two is pretty much like in English: either you have the pronoun before the noun min katt 'my cat' or you have a verb between them and the pronoun last: katten är min 'the cat is mine'.
Yes, 'levande' is another approved option. If you write something that is wrong, but more similar to another approved answer than to the 'best' answer, the machinery will try to match it with whatever is most similar to what you put. This means you may sometimes be shown answers that are OK, but not great, since we need to accept those in order not to make it too hard on users.
No, lever is the present tense so you can't use it with är - it would sound like "Is your grandfather lives?"
There's always "Is your grandfather living?", of course, for which we have levande, but it sounds a bit odd in either language, I'd say.
Also, as Arnauti noted above, lever means "liver" as well.