Jade should be freezing cold to the touch, but this certainly looks like jade and it certainly looks old. the only way to find out what the clasp is made of is to take it to a jeweler and have it tested. My best "guesstimate" of its age is 1900s - 1920s.
You should have the whole thing restrung, making sure that it is knotted between the beads, so you don't lose all of them if the necklace breaks.
If it is in very good condition, the current retail (replacement or insurance) value of is approximately $1,250. If you were to sell it, you could expect to get the fair market (private sale or auction) value of approximately 40% of the retail amount or $500, depending on location and actual condition.
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