Lithium-ion battery charging and discharging
1) If you discharge a battery, the voltage will go down.

2) Read the manufacturer's data sheet for the battery you have. 'A 3.2v battery' is not a sufficient specification for what it actually is, you need to know what precise chemistry the battery is using. Then, with your specification for how you want the battery to perform, so trading off maximum capacity with short cycle lifetime against less capacity but longer cycle lifetime, the battery data will tell you what cutoff voltage to use on discharge. 

If it's been suitably programmed, the Computerised battery analyser may well have set voltages for specific battery chemistries stored in it.