Re: Is this battery rechargeable?
I'll second most things written in this thread.
Also, about asking about batteries... every single forum I'm in that has batteries as on-topic, love questions about them, especially regarding safety. I've always had (and still have) the impression that's the case here on CPF as well, so please do ask if there ever is anything.
Other than that, I'm mostly stopping by this thread to stress the issue that LiIons are consumable items. If the question is "I have this 10 year old 18650 LiIon battery, and I'm wondering if it's rechargeable?", then the answer is "it was". ;-)
If you'll forgive the humorous phrasing, the point is real. Even a good LiIon battery that's been left to fend for itself can grow dangerous, and it's non-trivial to investigate for internal damage. It could short out internally during charging, or during use afterwards. If it goes rapid exothermic on you after charging, it'll do so with more eagerness and persistence than it would if you hadn't charged it.
If you're interested in the why and how, LiIon batteries that spend time at too low a voltage, can grow dendrites that can short them out internally. This is an even bigger problem when you bring self discharge into the picture, and 10 years (as in my example) is a lot of time for self discharge. Now, to make things even funnier, if you simply measure batteries with a multimeter, you can have an artificially high reading, making it hard to do even basic checks before charging. Dendrites aside, components can also degrade over time. Gaskets can fail or grow brittle (vulnerable to mechanical impact), and so on.
There are things you can do to check things out a bit more, but for most people it's just not worth it. Better to just get a high quality cell from a reputable dealer. Even if you went through all the hoops for doing a health check on it, bought the equipment, read up, did the work and so on, at the end of the day, at best you have an old battery with reduced capacity and reduced safety.