Watched your video. The part on your handlebars with two wires dangling looks like the mount for a wired speedometer (bike computer). You can find a wireless model for $5 shipped from China to USA, maybe higher to other countries. Your current battery is a 36 Volts and it's showing full charge at 42.33 volts, maybe a little high, as it should be 42.00.
What are you trying to do with the tool batteries ("two in series and two in parallel"). Are you getting them for a big discount? Their packaging would make four of them kind of cumbersome on a bike, in my opinion. You won't get any more speed. Maybe a different range.