Wiktionary has lahvemi with a short a. Is it wrong or are both ok?
Both are fine. I am not sure which one is the more common.
This is not a good English translation. There is technically nothing wrong with the sentence, but it would not be expressed this way. A more natural translation is "Where do you take the empty bottles." or "Where do the empty bottles go?"
This would result in a problem in the opposite direction. People would rightfully complain that the Czech sentence is not close enough to the English one.
This translation is not English, unless it means "Where should one take empty bottles?". Otherwise, it would have to be "Where are you going with the empty bottles?"
No. A different Czech verb (jít) would be used if the English sentence was in present continuous.