The way this works: Leave a comment, I'll reply to it with an answer, then place the answer into the deviation.
1. Q: "What're the fundamental values all Satanists believe or practice?"
A: Satanists believe in obtaining godhood/apotheosis through the genetic/spiritual modifications Satan gave to humanity; a process long forgotten and thought of now to be a "myth".
Unlike other belief systems, Satanism actually requires work... instead of sitting around all day playing video games or praying to some god. Godhood is obtained through power meditation, yoga (kundalini/hatha) and hard work, perseverance.
The other values Satanism promotes are knowledge, truth, justice, kindness, self-empowerment: and freedom of the mind, body, and soul.
2. Q: "If it helps, you can divide into the different branches, since I'm not sure what branches really believe. What I just know there's a few of them."
A: As for "branches", there are no branches of Satanism.
Either a person follows reality, or they are not a Satanist; LaVeyanism is LaVeyanism, Luciferianism is Luciferianism, and Satanism is Satanism.
3. Q: "If you were to place a simple description or definition of Satan, what would that be?"
A: A bit of a preface: the red "evil horned man look" is NOT AT ALL ACCURATE to how he looks... that is merely how his enemies portray him.
He is a tall blonde humanoid with electric blue eyes: tan-ish, strong jaw, well-built.
Usually I see him wearing a white robe: though sometimes he appears with armor, like a knight. Sometimes he also has ethereal-looking wings.
I've found that the hair length varies when I see him, but he always has the same general look to him.
His aura creates a calming effect, but also raises the atmospheric pressure of whichever building he appears in. I have a drawing of him in the Satanism section of my gallery.
As for describing him non-physically; he's very kind, understanding, supportive. He has never said anything negative to me or about me. He also has a great sense of humor, and knows when to relax. He cares deeply for humanity, and I hope we are reunited with him soon (he has stated to me personally that he is "coming to Earth".)
4. Q: "Could you also give a description of Lilith. I don't know to much about her other than she is a big supporter of women's rights."
A: Ah, Lilith, Satan's wife; She's a lovely woman.
Strangely my vision of her looked wildly different than the one portrayed on JoS;
Her hair is black and is styled somewhat similar to Asami's (Legend of Korra).
She has violet eyes that show kindness; her skin is a light color. She seems to wear a slight amount of makeup, but nothing too drastic. Of course, she's also very attractive.
5. Q: "How long have you been a Satanist?"
A: 4 years of being a dedicated Satanist, almost 4 1/2 of being a Satanist. I dedicated April 31st, 2011.
6. Q: "How did you come to Satanism?"
A: For the first 13 years of my life, 7 or so of those were spent as a christian... the first 5 or so I don't remember much at all. I never really got into christianity. maybe for a week or so, but that's it. I never felt the presence of any of the bullshit book's characters.
Around age 13 I stopped using fluoridated toothpaste, and honestly I think that's what led me to start questioning things (in addition to the "coming of age" thing.)
Age 16 I left christianity after various happenings, and realizing I had never seen any evidence AT ALL for christianity being legitimate... for 4 years I was lost, tried a few "occult" things, but nothing ever stuck with me. Every prayer felt like it was sent to a black hole, not any sort of god or person.
I also stupidly thought I was "possessed" during this time (which I have come to realize was just my own subconscious acting out.)
At age 19 I was introduced to the Joy of Satan website... it was a great awakening; looking at the page made me feel like I had finally found the giant, missing piece of the puzzle I had been desperately trying to assemble in my life. I felt guilty at first, but Satan reassured me that I was "home" now and comforted me; forgave me for being a bit foolish (the whole possession bit), as I didn't know any better.
About a week after that, I stood up to my abusive ex-stepfather; this lead to a chain of events in which I was moved out of the house and lived with the man who introduced me to the JoS site. I performed the dedication ritual about 3 months after that (I had turned 20.)