Could be either/or. I know many people that have had chicken pox twice and others that have had shingles. Just make sure you take some simple precautions, i.e don't do what my dad did when I had it, which was to finish my milk drink for me and then wonder why he caught chicken pox again lol!
Yes you can get it again, I caught it off my then 5 year old son even though I'd had it as a child. I went to the doctors saying 'this can't be chicken pox as I've already had it'. Oh yes it is she said!
Yes, you can get chicken pox mor than once. Shingles is related, but doesn't mean you're going to get that instead of CP just because you've already had the childhood ailment already.