Here is some Slavic linguistics for you: "ż" is an etymological letter used in words where in other Slavic languages the sound is and has initially been [ʒ] (żona - жена), while "rz" evolved from what had been initially a palatalized "r", which is the case in languages like Ukrainian or Russian (rzepa - репа).
dobrze is an adverb, in English "well" or "fine." How are you? Dobrze. I am well.
Dobre is a gender-neuter adjective, in English "good," but used with a gender-neuter noun, such as dobre miasto, "good city," or a plural noun, such as dobre miasta, "good cities," but not a plural noun that includes at least one male person, which uses dobrzy.