Translation:I see the children and they are all happy.
In formal speach and in writing, yes. In daily talk nobody bothers and it sounds pretentious if someone does.
Does it technically mean "and everyone's happy"? Such that you could be talking about two different groups here " I see the kids, also, everyone is happy". If so how would you link the second half to the first half of the sentence? "והם כולם שמחים"?
I think כולם is literally something like "all of them", so here it really does refer to the first subject הילדים, not a general ambiguous "everyone".
They have nikudot in the given answer to reduce ambiguity (רואֶה vs רואָה). Just ignore the "typo" like you ignore it when they try to correct "youre" to "you're"
could שמיחים also be translated into "rejoice"? If not, is there another modern hebrew word for rejoice?
I see the children and they are all happy. This sentence does not make sense in English, I do not get it.