Without context, should "Hallgatok" be accepted as well ?
Probably not. Hallgat is a better match for "listen" than "hear" - it is something you do consciously as an activity.
That is correct. "Hallgatni" is "to listen". There is that "-gat" suffix in there that makes this a listening activity.
"Hallgatni" can also mean "to stay quiet". Even as a command:
"Hallgass!" - "Be quiet!"
Wouldn't „hallgass!” be "listen up!"?
As he says, hallgat is also used to mean "be quiet", and hallgass is a pretty commonly-heard command to be quiet. It's more polite than the rather rude kuss! ("shut up!"), but it still means "be quiet."
Hallok és hallom is lehet az 'I hear'.
You would translate hallom rather with "I hear it."
The correct translation is: Hallok, without én.
The én is fine as well.