"While doing homework, he watches television."
Translation:Farante hejmtaskojn, li televidas.
Why is "hejmtaskojn" plural? He was doing homework. That's work, not works. He may have had only one assignment in any event. In other sentences it was just "hejmtasko" (singular).
English looks at it as a big glob of "work" to do, while Esperanto looks at it as individual "tasks" or assignments.
If he had had only one assignment for his homework, "hejmtasko" would be appropriate. But if he had been assigned "questions 10 to 14 on page 365", then "hejmtaskoj" would be right.
Maybe he had multiple assignments from different classes. In English we usually refer to all of it together as a single entity, but in other languages, they make a distinction between different tasks, and so pluralize the word.
To essentially say "He did his homeworks" in other languages is perfectly correct.
This way is more concise. With "dum" the sentence would be "Dum farado de hejmtaskoj, li televidas".
dankon. But should it be accepted even if not concise? Also is homework always plural? For example "I do not have any homework tonight"
It's probably lesson about participles so they are used in sentences. "Hejmtasko" means "home task" so if there are a few tasks they are called "hejmtaskoj".
In my experience, it's usually plural, because usually you get more than one question/task/assignment as homework.
"Mi ne havas hejmtaskon ĉi-vespere" implies to me that you do not have an assignment tonight but that you usually have exactly one.
So I would expect "Mi ne havas hejmtaskojn ĉi-vespere" (plural) to indicate that you have no assignments tonight but that you usually have multiple assignments. (E.g. "question 10-14 on page 365".)
IMO using "Dum" viz., "Dum farante de hejmtaskoj..." is grammatical and thus perfectly acceptable.
That looks to me like a straight translation from the English "while doing of homework".
I think dum has to be a preposition, followed by a noun (dum la farado de hejmtaskoj) or a conjunction, followed by a clause (dum li faris la hejmtaskojn, ... or dum li estis faranta la hejmtaskojn) -- and that second is, I think that "while doing the homework" is short for ("while he was doing the homework").
But I don't see how you can combine dum with an adverb such as farante.