"They have nothing to drink."
Translation:Nemají co pít.
Please help me to understand why co is the preferred word instead of nic.
You cannot just put "nic" in the sentence formulated as the answer above. You can say "Nemají nic k pití.". That is fine and it is an exact word-to-word translation.
The difference is that you can use the with infinitive like "Nemám co dělat."/"I have nothing to do." while you use "k" and the verbal noun "pití" with "nic".
I had thought it was normal to use "za" before verbs, like Nemám nic za jít. Is "za" used in any such situations?
I can't think of any such possibility, "za" is used in front of an object irrespective of the verb.
Theoretically you can say "Nemají za co pít." where the za binds with co. It means they have no money for drinks.