Does LiPo4 battery amperage output increase as voltage decreases from 4.2V to 3.57? I'm trying to size up a diode
Dividing energy [Watt-hours] by voltage [V] does not give amps [I], you have to divide power by voltage to get amps.  The power output is V*I with voltage determined by the battery and current output determined by the load.  The current capacity of the battery pack is not specified by the energy capacity but you can calculate it if you have the C rating.

A 100Whr battery can deliver 100 watts for 1 hour or 10 watts for 10 hours, it depends on the load. The voltage will decrease as the battery discharges and for a fixed resistive load the current will also decrease according to Ohm's law.

As far as needing a diode, it sounds like your charger is not correctly configured for the battery pack.  The only way for the battery to source current into the charger is if the charger voltage is lower than the battery voltage.  No charging will ever happen if that is true.