How long do I keep...

I have a couple things floating around, and I didn't see anything on the website mentioning use-by dates... unless I missed it, which is quite possible. So first of all, frozen mochi. I bought it for Tanabata (July 7) and used it up one by one, so the leftovers have never been thawed. How long does it last? It's unflavored. Used for moffles, which are amazing. Second, I have canned tsubushi-an (because I gave in to laziness and didn't make my own... and I couldn't find azuki beans!) that is open, but covered, and I put it in the fridge for some reason... I'm probably not going to use it with any real frequency, because I'm the only person who eats it. Third, kitsune, which is actually aburaage, I think? It's inari wrappers so it's flavored/seasoned/drenched with yummy goodness. My brother makes a mean inari. But I digress. Last is umeboshi! I don't have experience with keeping any kind of pickled thing! My dad does, but he has an iron stomach and I don't trust him. These are refrigerated right now. I'm still getting re-used to them, so they might be there a while. If anyone knows how long I can keep these, I'd appreciate it! I'm a bit paranoid about food going bad, which is probably partly my dad's fault. He's the 'experimental' cook of the family. Good at it though. Too bad it isn't hereditary. :(
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