Think of this as meaning, "To them it is good." Notice that "хорошо" is neuter? So something else is implied; essentially, "им (это) хорошо". The same principle works with:
Им холодно -> To them it is cold. -> They are / feel cold.
Им жарко. -> To them it is it hot. -> They are / feel hot.
«Я хорошо́» means 'I'm good' said by someone who is of the neuter gender. E.g. imagine a fairy tale where a sun is personified and speaks about itself.
In real life, living people don't use neuter pronouns (and it's pretty dehumanising to use neuter pronouns about someone, because neuter is usually used for lifeless things), but feminine «Я хороша́» 'I'm good' and masculine «Я хоро́ш» 'I'm good' sound OK. However, you're more likely to hear them with «ты», e.g. «Ты хороша!»/«Ты хоро́ш!» as a form of praise. (It can also be used sarcastically sometimes.)
«Они хорошо́» doesn't make sense, since они́ is plural, and хорошо́ is either a singular neuter adjective (in its short form), or adverb, or predicative verb. But «они́ хороши́» 'They're good' (as a form of praise) works.
Note that those are short forms of the adjective «хоро́ший». Long forms are used with a slightly different connotation. «Они хороши́» brings up images of someone doing things well, but the long form «Они хоро́шие» brings up images of well-behaved children or someone behaving in a kind and naïve way.
Can "It’s good for them" mean that they feel good? If so, it should be accepted.
But I’ve only seen it used differently, meaning that some thing or event is good for someone (or maybe not really good, because the phrase is often used in sarcastic way). This is not the meaning of the Russian sentence. If this is the only meaning the English sentence can have, then it shouldn’t be accepted.
I.e., the Russian sentence doesn’t refer to anything in particular. «Хорошо» is not a thing or event, хорошо is a generic reference to the current state of things.
Yes, as 'well' is an adverb and should be used to describe how someone is feeling or being. 'Good' is an adjective, used to describe a noun. I would probably say, "They are ok" rather than good. This us something English speakers get wrong every day. "How are you?" "Good thanks".
I've been tryingout busuu but I must admit, without the stuff I have gained from Duo, it would be an uphill battle (well more than it is) so my suggeston is to glean as much as you can from Duo (and whatever other systems are out there). So, yes, I find that I am not enjoying this as much as before, but that could be me reaching a plateau peppered with some very petty people on here. But the diamonds who also try to help really are priceless.