Satan was originally a Hebrew term. It was a title not a name, as are most names such as Michael, Raphael, Gabriel, etc. They are titles that many sentient beings end up standing in the role of. Even Eliphas Levi (an Ex-Catholic Priest that moonlighted as a Ceremonial Magician) brings this up in one of his many books (I'm sorry I can't recall the exact one).
Satan meant adversary but more specifically, in Jewish myth, the one with the title was the one that created yetzer hara, which basically means temptation or an urge toward evil. Yetzer hatov was the good acts inspiration. Yahweh had the yetzer hara used in a way to test and teach and the one that did this was so titled Satan. But Christianity comes in and claims Satan is sentient and that's his name. Satanists jump on this bandwagon and here we are.
So your "Father" is a mystery. You need to figure out for yourself who it is you have been working with. Sit down and meditate on it and maybe you'll get clues that point you in a better direction. For all you know it is Pan, Cernunnos, or the general "Ol' Horney One" that witches so lovingly call Him. That is the "Horned One" aka "Lord" of the "Lord and Lady" gender duality of Deity. As a type of spirit they can be associated with satyrs more so than "demon".