Charging Li-Ion with BMS and CC-CV DC converter
I somewhere read, that CC-CV is from an electronics point of view
  simply CC, so the voltage might vary.


CC-CV stands for Constant Current and Constant Voltage, which means both voltage and current are regulated. If the battery does not accept the set current then the voltage will be held constant and the current must go down. This is the standard charge profile for Li-ion.


  Are there fatal consequences to be expected, if the converter is
  connected for too long? What happens in that case?


The booster should continue to hold the battery voltage constant forever, and the battery should handle this. However at maximum voltage the battery's lifespan is reduced, particularly at high ambient temperature. An hour or two at full voltage is fine, a week is not. If you have to float continuously then reducing the voltage from 4.20V to 4.15V or 4.10V will increase lifespan with some reduction in capacity.    

To check that the booster maintains a safe voltage, simply set it to the correct voltage with no load. Then charge a battery with it and measure the voltage regularly as it gets close to the end. It should not go above 4.20V per cell. 


  there might be a chance that the CC-CV converter... puts out more than
  42V which is definitely a hazard for the Li-Ion cells. But since I am
  using a BMS (with overvoltage and balancing capabilities) I should be
  safe from this, right?


Yes, in the unlikely event that the charger malfunctions the BMS should disconnect the battery before any serious harm occurs. However to avoid interfering with charging the BMS must cut off at a higher voltage than the normal peak voltage, so there is still a chance of cell damage occurring. Also some BMS circuits have an uncomfortably high cutoff voltage that may not be very accurate. 


  Are BM systems in general capable of doing overcharge protection?
  voltage- and current-wise? So simply put: Can I connect the BMS to CV
  42V and it will take care of everything?


Most BMS circuits protect against over and under voltage and over-current. This should protect the battery from catastrophic failure of the charger or device being powered. It won't prevent long-term damage due to consistent floating at maximum voltage, drawing high current, discharging below the normal cutoff voltage or charging at a high rate when the battery is deeply discharged.

If the BMS has balancing then it should be able to maintain balance provided that the cells are fairly well balanced to start with, and the charge current is not higher than the balancing current. For the first charge you should measure cell voltages regularly and reduce the charge current if they are not all within +-0.03V of each other. Balancing may take several hours if the imbalance is more than a few tenths of a volt.