Use cell phone batteries as a battery pack
Cellphone batteries are optimized for safety, capacity, and cycle count performance. In that area they are pretty good, since if there were a better technology or chemistry, manufacturers would have used that and presented it as a competitive advantage.
I've seen both, so it varies. Testing is not too hard, but it can be somewhat time-consuming.
Discharge the battery to say 2.8 volts (via a power resistor for example) and continue monitoring its voltage as it winds down even further. If at some point the voltage goes to 0V abruptly, then it's because of the protection circuit. I'd discharge it to 2.4 and if it's still not 0V, it's likely an unprotected cell. This assumes that the overdischarge threshold is somewhere in 2.5-2.8 volts, but the exact value depends on the protection IC used, and can be lower than that, as this thread indicates (2.0V on the BL-5C). I do not recommend that you discharge to less than 2.0V "just to be sure", this will be almost sure to permanently damage the cell.