testing chargers?

I am being given some probably noname chargers, and need to decide if they are safe to use. I’ve got a few questions.

First off a protected battery question.
In theory, if its working properly, the protection circuit will disconect the cell before it has suffered damage, is this correct?
I realise its not good to run into the failsafes, but at worst testing with a protected battery will just shorten the battery’s life span a little and not cause it to be dangerous?

Now onto the chargers.
As far as I can tell noname chargers can have several problems,

*Overvoltage
*not terminating

How do I tell what the max voltage a charger will go to? Is this just the open circuit voltage, without a battery?

If the max voltage is 4.2v or less what is the need to terminate? It may take a long time to fully charge, but its never going to charge to more than the chargers max voltage.
I’ve seen that a lot of chargers, even good ones, use a higher ConstantVoltage than 4.2v so as to charge quicker, and need to terminate before the battery goes over 4.2v.

Assuming they have both these problems, has anyone modded these to be safe? How?

TIA