meddling with phone battery and charger
Batteries contain energy and chemicals and those two things generally tends to be unsafe.

A good battery should contain functionality to stop bad things to happen, such as thermal shutdown and short circuit detection. But do not count on it, even big companies (mentioning no name) have problems with batteries getting too hot. Li-ion batteries does not like getting hot. Some batteries (old models) will even explode directly in your face if you short circuit them and I am speaking from personal experience here.

You should not go beyond the maximum rating for the battery. The maximum ratings for the battery can be stated by the vendor together with the model of the battery in question. If you do not have this information I strongly advice against you using it.

There are a myriad of different battery management chips that you can use to charge Li-ion based batteries. The hard thing is to get a chip is suitable for the battery you would like to charge. Normally the specification or battery manual will point you in the right direction.