What exactly is the function of "to" in this sentence?
It is kind of as if you said "what IS IT you are carrying?" You are specifically asking about that something you see the person bringing.
Thanks for the quick reply!
Is it at all acceptable to just ask "Co neseš?" or does that sound unnatural?
Yes. You can. It is tiny bit more natural with TO but in some situations it is perfectly fine to skip that
Can it be as in russian "what are you talking about?"
Would the negative of neseš be neneseš?
"What do you carry " is wrong answer, tho it is said that czech doesn't have continuous time
can it mean "what are you bringing?"
Literally more like "Co to přinášíš?" The golden rule of Duolingo asks to be as close as possible.