Dobranoc is one word. Similar to English where "good-night" is one word, at least in relation to the farewell. You would use "good night" as a formal, (rarely used) greeting, but "good-night" as a farewell. (Remember, in Polish the stressed syllable is always the second to last in a word.)
Dzień dobry are two separate words. Again, similar to english: "Good day" or "Good morning."
You can rarely compare the two languages but this is an example that lines up. I hope that helps.
"Dobrzy" is a masculine personal plural nominative form of "dobry", i.e. you use it to describe several men who are fine/good. I guess if the word "fine" is given without context, it can be translated to all possible forms, but in a sentence like this one you need not an adjective, but an adverb, which is always "dobrze" (note the E).