Ask an ex-mormon nerd

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Does the church claim to have the plates and stones? Can they be seen?

What is the big deal with genealogy?

Did you wear the magic underwear?

Question 1: No, supposedly they were taken to heaven, as per the word of mainstream mormonism which is the sect I was raised in. 

Question 2: Mainly for the uses of temple work, ie: baptisms, confirmations, and sealings (mormon covenant for married members) for the dead which is crucial to the doctrine since families are for eternity but they must be members to be together forever in the highest degree of heaven. Then, also, for the reasonable humanistic need to feel connected to one's heritage and history...but it's mostly driven by religious needs. 

Questions 3: No, I never received my first covenant of "endowment" in the temple so I was never required to wear it. If I had done endowments, then yes, I would have.