None of those could ever be correct, unless someone made a big typo when putting the acceptable answers in the Incubator.
"dobry" is masculine singular - so "dobry człowiek", for example.
"dobre" is either neuter singular (dobre dziecko) or 'not masculine-personal' plural. So for example "dobre kobiety", as the word "women" clearly states that there are no men in that group.
For "people", logically you have 'at least one man' in the group. So the word "ludzie" is masculine personal. And the masculine personal adjective is usually quite different from the other forms. So here, it's "dobrzy", changing R to RZ.
In order to avoid much stress, be familiar with the genders. Generally speaking, words ending in a consonant are masculine, and words ending in vowels are feminine. Words ending in -o are neuter. Use this understanding to choose the proper forms. Everything must agree with each other in number and gender. Hope this helped
To be more specific
Nouns ending with vovels other than -a are always neuter
Nouns ending with "hard" consonant are masculine
Nouns ending with "a" are mostly feminine, but there are some masculine exceptions, those describe male persons.
Nouns ending withs "soft" or "mixed" consonant like ś, ć ń , sz, cz, ż, can be either feminine or masculine and checking a dictionary is the safest way of checking
I can explain why not -e : dobre is plural not masculine personal, dobrzy is plural masculine personal
Ludzie is plural masculine personal noun, so we use plural masculine personal adjective.
dobrze is adverb
-y and -i endings depend on the last letters of the adjective , but I do not remember the rules. ( I think most -ry ending masculine adjectives change to -rzy in plural masculine personal)
"dobrze" is not an adjective, it's an adverb ("well", "fine", sometimes even "okay". So "Dobrze, ludzie" could be "Okay, people".
"ludzie" is a plural noun - a 'masculine personal plural' one. This means that it describes a group of people including at least one man. The right form for that plural is "dobrzy". The second plural, the 'not masculine-personal plural' one, is for every other noun. The right form for it would be "dobre".
"dobri loudly" to me looks like it's Czech (although I know almost nothing about Czech). It's definitely not Polish, I'm afraid.