As I said, the DSD is far from being a good charger, I'd pretty much rate it in the POS category.

They usually have an open circuit voltage between 5-6 Volts. The reason it varies when you take a reading, is due to the electronics involved. A proper charger will never expose the cell to more than ~4.25 (ideally, 4.20) Volts, so yes, this means there is no protection built into the charger. That said, most of the "cheapo" chargers have an improper voltage, as they don't use a proper algorithm.
From your voltage tests, I would conclude that your problem cell has a defective protection circuit. It is not allowing proper current flow into, or out of the cell. I would give up on it. It may, or may not be safe, but in any case, it isn't good for anything anyway.
Now that you have a DMM, if you haven't already, you may want to give
HKJ's thread a look, as it pertains to using one with flashlights/torches. Also, I don't know how familiar you are with Li-Ion cells in general, but I would strongly recommend reading the threads relevant to Li-Ion cells, in the "
Threads of Interest" sticky and, the "
Smoke and Fire" threads at the top of this forum. Knowledge is wisdom and wisdom is ..... I can never remember the rest of it, but you'll be safer and a lot better off, the more you know about them.
Dave