It sounds to me like the roller clutch is slipping. the rollers ride up a ramp until they're wedged when the motor starts to rotate. For whatever reason, at low torque, there isn't enough oomph to wedge them. Possible reasons: 1. Water has got in through the cable entry point - normally because the cable doesn't go down from the exit before going up to the controller - and so the clutch has gone rusty. Yours goes down so maybe OK. That would also account for other general noise. 2. lack of grease causing general dryness and unsmooth operation especially if it hadn't been used for a while before you got it. 3. Other contamination like a bit of dirt in the clutch.
If it's reason no 2, it might go away as soon as you start using it. If it's 1, then the motor has to be opened up which isn't too difficult on these. I haven't needed to do one yet, but I believe that you just remove the screws around the periphery of the side plate and tap it apart after removing nuts etc from the shaft. Whatever the reason, It would be a good idea to open it up and re-grease everything and then it'll be as smooth as silk and all the worrying will be over.
I can't see a hall sensor connection, so it's probably a sensorless controller, which accounts for the ticking and juddering at the start, Nothing to worry about there.
Regarding the battery,, which is made of 10 groups of 3.7v cylindrical cells, 9 per group from what I can see in the photo (edit: or are they 3 per group prismatic cells?) I think you need to charge it up and check that all the cells reach the same voltage of about 4.2v. They should all be equal within 0.05v if the BMS does its job properly. Then run it down about halfway and check the cell voltages again. The cells are in groups, so any one in a group could be faulty so that one group will go down quicker than the others. So.if it goes way out of balance as the pack voltage falls, you can identify the group and then check all the connections within the group.That means at each end of each cell plus the BMS wire. If all connections are OK, then it's faulty cells.
