I mean that your external power supply will just provide the 5v to the internal charger, the charging is controlled by this internal circuit so even if you connect a 5v/10A source the internal charger will still use a small percentage of this current to load the battery.
Lithium battery charges in constant current and constant voltage stages ( ), the value of the constant current is not controlled by you but from the phone manufacturer and the circuit/code he has implemented internally.
7805 has a typical voltage drop of 2v so you will need 7v input min. in order to get 5v output , if the input is lower then the output will drop.
I would suggest four regulators so that the consumption on the regulators is shared too, you will get up to 2v*1A=2W on each regulator so you will probably be OK even without any heatsink but a small heatsink would weep the regulators cooler.