Is this in the instrumental case? Isn't that needed here?
I think that's an adjective, not a noun.
Instr. is dorosłym.
You are right, „dorosły” here has adjectival role and therefore requires nominative.
I chose dorosli and it accepted my answer saying I made a typo - I probably should’ve been marked wrong ...
Why is not dorosłym the correct answer? Why does dorosły work? Is it because there is no noun coming after it?
"dorosły" is mostly treated like an adjective in Polish. "dorosłym" would treat it as a noun, and while it may not be wrong, I'd say it sounds rather strang here.