I'm curious if "ty" MUST be part of this sentence, or if it's there because the (unknown) speaker is saying, "Do YOU want to take it there?" (I may make an experiment if I see this one again soon...)
It's used for emphasis.
The other option is correct.
If you were to put a noun in place of "it", how would the word order work? Putting the noun after chceš sounds strange to me but I'm no expert.
To is a clitic so it comes to the second position. Otherwise, it sounds better to put the object "tam", but putting it in front of it is not impossible.
Why is 'Do you want to bring it there?' marked as an incorrect translation?
I'm no expert but I think because nést means carry whereas bring would be přinést.
I tend to agree in this case that it would call for a perfective verb.