Yes it does, for example, at a picnic, "I don't know who these big sandwiches belong to... Whose sandwiches are big?"
Maybe in a commercial. Singing: "Whose sandwiches are big? Homer's Homemade Hoagies'!"
Admittedly it would hard to score but that's a result of bad metre rather than bad grammar.
No. In your question, the subject is "the big sandwiches", and in the original question, the subject is "whose sandwiches".
So I'd translate your question as "Czyje są duże kanapki?", but it'd make a lot more sense to treat "the" as "these" and ask "Czyje są te duże kanapki?"
"Who's" means "Who is" or "Who has". "Whose" is a word on its own with different meaning
"czyi" - masculine personal plural.
"czyje" - not masculine-personal plural. And neuter singular.
If you meant "te" and "tej" is just a typo, then it's ok. Well, after you change "sa" into "są" of course :)
But it means "Whose are these big sandwiches", so it's not exactly the same thing. Even though it actually makes more sense as a sentence.
I used large on purpose to see if it would be accepted, I feel it should be. ?