As far as issue #1 goes.
If the charger output is 5V let's say, and when you start charging the battery it is at 4V. Depending on how low the battery voltage is, it will use more amps until it starts getting charged. The closer the battery gets to 5V the less amps it uses. So essentially it charges quickly at first, and then slows down as it gets close to being fully charged.
But when the voltage of the battery matches the voltage output of the charger, the battery stops pulling amps, i.e. it quits charging automatically. There is no need for any electronic brains to tell it to do this. It's just the nature of batteries and how they charge.