I think Yosef HaTsadiq and Eliyahu HaNavi had payoth because its said that they curled their hair.
People also curl their regular hair because it is stylish. And likely it was stylish for men back then too.
Payoth must be curled
Not necessarily. Only according to certain people's definition of payoth, which they invented. Any type of sideburn that is long enough to grasp with the fingertips (go with a #2 or higher, a #1 or a buzz cut probably is too short) is sufficient to be called "payoth" or in reality, to fit with the negative commandment that a person should not shave the corners of his head. That is what the Torah speaks about. A prohibition to shave the corners of the head (in the area of the so-called "payoth" but it is not termed that way). If you have thin trimmed sideburns (and they don't have to go below the ear, either), you have successfully avoided this transgression. What you are speaking about is a custom that developed later in Jewish history and is not necessary for a Jew to keep in order to be a practicing and kosher Jew.
so that they don’t mix with the beard hair. The head hair is Gevurah and the beard hair is Hesed so the 2 types of hair must never mix.
Interesting Kaballah, but the Vilna Gaon was also a kabbalist and had his own take on these matters, and he never said a person must have chassidic style curly-q's in order to avoid the transgression against shaving the corners of the head. And non-Chassidic Orthodox did not have the "payoth" you describe (those of the chassidim). Not that there's anything wrong with having them, but don't try to claim that this goes back to Sinai and that all Jews "MUST" keep them. Because it doesn't and they don't. There are far more important things and things that Jews really DO need to keep that they are not keeping. So why all this fuss over something not necessary? Anyway, it reflects poorly to suggest such things without basis in fact and claim that it's Torah-true.
I think Bereishith 27:3 implies that Esaw had payoth.
Sounds like you just made that up.
When Yitshaq sent Esaw out hunting he told him to take his bow and his teliekha. The word “teli” implies curled or dangling. A reference to Esaw’s payoth?
What?!