No you got it wrong. There is indeed a masculine and a feminine for the word "meilleur" (which becomes "meilleure" in the feminine form) but mieux is an adverb, it doesn't have a feminine form, it never change. Now that said, mieux and meilleur are not interchangeable. - "mieux" is for describing something "well" and "meilleur" is for something "good". - "mieux" uis to modify a verb, "meilleur" is to modify a noun. So if you want to say something works best, you want to modify "to work" (and that implies this works WELL), you say "il fonctionne le mieux". And if to say something is the best, you want to modify a noun, (that implies it' s good thing), yo say ."il est le meilleur". or in the feminine form "elle est la meilleure."

Yes, Meilleur est masculin et meilleure féminin. Ex: She's the best dog - Elle est la meilleure chienne. He's the best dog - Il est le meilleur chien