From the perspective of an outsider, what makes this belief special compared to other mainstream options?
It's not a "belief", it's a path of transformation. If you noticed, the main point in SS is to work on your soul, transform it, open your astral senses and raise your kundalini and become a God. It's not comparable to blind faith religions. If you want to compare to something, try esoteric and occult paths. It's more similar to them than mainstream religions. Following Satanism like a mainstream religion with a different god will get you nowhere.
Do we trust someone's judgement?
No. You are free to not accept anything until you ask the Gods to confirm it.
Sure, christians worship a fake idol, but how do we know we don't?
Because "we" (you are an outsider so you aren't one of us, no offense) do not worship anybody. Satanism is a path of transformation, not worship.
Where are our Gods? How did They came to be? Why do they have all of these powers?
You have to read the JoS, it explains all that.
I would like to find a more comprehensive guide on Spiritual Satanism that is not a website that reads like a blogpost.
The JoS is as comprehensive as it can be. Over 1,000 pages of material, if you print it. And this doesn't even include the sermons and PDFs in Satan's Library.
How do we know that the things in there came right from the Gods? Everyone can claim a "god" spoke to them like jewsus or muhammad for their respective religions, so what would make this one different?
If you read the site, it says that you can ask the Gods directly. You can communicate with the Gods and ask them. You probably have the wrong idea. Reread the first paragraph of my reply to see what Satanism is about. It's focused on transformation of your soul and experiencing things for yourself, not believing.
You can try all these meditation techniques, open yourself to the astral and ask the Gods.
Do you place your faith blindly, or do you have tangible proof that they exist?
See above. Many of us have close, personal relationships with our Guardian Demon and other Gods.
Why do They have multiple names depending on the civilization?
Because they were the same beings but they were known under different names depending on the different cultures.
How do we know Baalzebul is Zeus, for example?
Compare their mythologies, many things are common between them. Baal a.k.a. Baal Zebul was a Sky and Thunder God just like Zeus. There's an entire field of study called "comparative mythology" which shows the parallels and similarities on gods in different pantheons. Besides asking the Gods themselves, obviously.
I think a bit of skepticism is much needed when dealing with the spiritual.
Using your left brain is not needed. What is needed is to be open and try things yourself.
Unlike Christians, nobody asks you here to believe anything you haven't experienced. Satanism is an experiential path. It's based on practice and experience and communication with the Gods.
You're not asked to believe everything you read, obviously. You're asked to try the practices and see for yourself. Practicing is the most important thing here. Intellectual philosophizing will get you nowhere.