Is "and" elided in the sentence?
Your first expansion seems correct to me, but 2 is a misinterpretation. "the rest" means all the other institutions based on the supernatural. This is the idea that the authors' "beliefs" can be grouped together with all the other "superstitions" because they are both concepts relating to the supernatural.
It sounds like the author is demonstrating that different beliefs (or maybe even religions) should be considered altogether as one concept: "the supernatural". The word "superstition" has a slight derogatory tone when used alongside "belief". It's as if the author has been deriding his neighbour's beliefs but has now come to the conclusion that they are very similar to his own.
Beware the meaning of premises. It can be the plural of "premise" (part of an argument) as well as buildings and land.
Yes, your paraphrase captures exactly the meaning. However, grammatically, I don't think there is any implicit conjunction "and" here. Rather, there is a suppressed "with", as when you are considering two things together, you consider a first thing together with another thing. The writer could have said "with our own considered among the rest".
No, "the rest" does not mean "ours only". But this is obvious, so I'm not sure I've understood your question.
It seems the writer is trying to avoid suggesting that our own religions are mere superstitions by appealing to some higher level category which encompasses both "true" religion and superstition. (It is not a successful attempt, in my opinion.)