"Where are you carrying those hats?"
Translation:Kam neseš ty klobouky?
Really? So you can't say "Where are you going?" Do you always have to add "to" at the end? I don't think so.
Ever since English stopped distinguishing between "whither" and "where", the word "where" can be used for both meanings. Adding "to" (for kam/whither) is only for emphasis, similiar to adding "at" (for kde/where), like "Where are you at?"
Motion may be involved with "kde" as well as "kam", the difference is whether you're talking about the direction/goal of the motion. Consider these two examples:
"Praha je město, kde jezdí hodně aut." - lit. "Prague is a city where a lot of cars go." - meaning there's a lot of traffic within the city, we're describing a motion, but it's confined to the place, there's no direction.
"Praha je město, kam jezdí hodně aut." - "Prague is a city, where a lot of cars go (to)." - meaning a lot of cars travel TO Prague from other places. Older English would use "whither" here instead of "where".
The sentence "Kde nosíš ty klobouky?" is grammatical (with the verb's aspect switched to imperfective though), but it's funny/nonsensical, because it's referring to a person carrying hats perhaps in a circle or to and fro. With "kam", it works in both aspects ("Kam neseš/nosíš klobouky?") and it makes sense.
Good question. You are more or less correct. Though... But...
Kam nosíš ty klobouky, could only be used as a translation of the English sentence when I am witnessing you walking by me, for the third time in last five minutes, every time with a different hat. You are currently on the way for the fourth, you are not carrying one now but it still is an ongoing event and would use continuous tense.
If the opposite translation was based on "kam nosíš ty klobouky", then "..wearing.. " also would have been a possible variant. The opposite exercise is based on the "..neseš.." sentence though so we do not have to go that far.