SOLAR CONTROLLER 5V - turn EN by default to LOW

Actually not 5V.  Normally the EN pin is jumpered with BAT which is the battery voltage. 

LiPo is nominally 3.7V but generally goes up to 4.2V when full.  However a LiPo battery's voltage drops as the battery is discharged … leaving me wondering how low the EN (EV_VOUT) voltage is expected to drop ?  What is the lowest BAT voltage at which EN is active (the Solar Power Manager tries to deliver 5V to these pins) ?

Does DFRobot require that the battery cuts off when it reaches a certain voltage ?

EN can be seen as an input pin.
EN controls a MOSFET, and the 5V output of the Solar power manager will only be enabled when the EN input is high. If your ALARM camera can output 5V and 0V, you can connect the GND of the ALARM camera to the GND of the blue pin of the Solar Power Manager, and then connect the ALARM signal output line to EN.

EN by default is HIGH and I would like to turn it LOW … So I can control it with my ALARM camera ON/OFF