High Short-circuit protection for LiPo Battery
What if I have a charger that malfunctions and does not regulate the
  charging current correctly, but has a current limitation of 0.5A.
  Could I not then have a constant 0.5A going into my battery for which
  the short-circuit protection does not protect for, and that my small
  battery would most likely not survive?


Lipo batteries generally have higher rated discharge current than charge current. The PCM current limit is supposed to protect against over-current during discharge. It is not designed to prevent charging at a lower current that might damage the cell.

Charging at a current over the cell's rating probably won't destroy it, but the cycle life will be reduced. The greater danger with Lipos is charging over 4.2V, as this will blow it up! Your PCM cuts at 4.27~4.28V, so it should prevent this catastrophe if the charger malfunctions.       

For such a small cell the PCM's over-current rating may be too high to protect it in all circumstances, however the safety risk is also low for a battery this size. The PCM has a separate 'short circuit' protection that should protect against very high current draw  (a useful feature, because it's very easy to accidentally short the leads when working with these tiny cells!).