Learn English – Should I use “another” or “other” in this sentence

All of those options are fairly natural, though, as you suspected, the repetition of the noun "group" in the first comes across as a bit awkward. "Others" is certainly not limited to people, and the third option seems like the most likely for a native speaker to produce.

As you note, "key" can be either a noun or an adjective.

If you use "key" before a noun, it is usually understood to be an adjective. "Honesty is the key attribute that we are looking for." "Attribute" is a noun. "Key" is modifying this noun.

If "key" is used without a noun to modify, it is usually a noun. "The key to the door is in the drawer." "Key" is not modifying any noun, so it is a noun itself.

Words like this get tricky with predicate adjectives and predicate nominatives. But in general, if there's an article, then it must be a predicate nominate because predicate adjectives don't take articles. So in, "The hint is the key", "key" must be a noun because it has an article. In, "The hint is key", "key" must be an adjective because it doesn't have an article.

But this can be trickier still because we sometimes omit nouns that are repeated. Like, "Honesty is usually the most important factor and competence is the most obvious, but in this case good looks is the key." "Key" here could be a noun, but it could also be an adjective with the noun "factor" omitted. (I suppose in this case the sentence means essentially the same thing either way so it doesn't matter.)