I've figured I need a 18650 style 2S2P battery with 40A continuous to fit my needs, I have found the cells.
I will charge the cells individually on a dedicated charger and load them in the robot using a battery holder (rewired to a 2S2P configuration) (see picture below).
The question is do I need to protect each individual cell from over discharge, or each 2P group or the battery as a whole? And where should I start to try and design the kind of circuit that can take the 40 amps?
Is over current protection necessary?
The answer is maybe. The answer to the question you didn't ask is NO. That question is 'is it safe to connect these batteries in parallel'.
You have demonstrated enough knowledge that I can assume you have a proper charger with all the required charging protections (I use SkyRC chargers only, one for balance charging, one for all cylindrical, and a big balance charger for >5000 mAh packs)
There is a lot of information on the net about this, but be warned a lot is wrong. For a 'mech warfare' robot you should probably get something like the following. https://amz.run/9VsG
and this charger https://bityl.co/RrRY
Good luck.
"Safe" can be "for the life of the cell" as well as "so your experiment does not burn the block down."
EV battery cells are matched in capacity and internal resistance so they all charge at the same rate to the same level, and discharge at the same rate to the same level. Mis-matched cells would charge and discharge at different rates to different levels. This causes imbalance in current and full-to-empty use, and eventually effect capacity.
Batteries have fires, but only due to negligence. Most battery fires do not occur while charging or discharging, rather, during storage while overcharged. I have charged thousands, without issue. Laptop computers would be banned from the world if battery fires statistically occurred.
I intentionally over-stressed a factory balanced battery, which over-heated, expanded, broke membranes, started smoking... until I smothered it... to avoid a fire. That is the only balanced batteries I have experience being destroyed (three have "melted" from heat, none have caught fire) in a decade of working around EVs, and I have seen some serious physical abuse.
If you have balanced batteries, in parallel and series, with a BMS, do not worry.
Also, that battery holder with springs and tiny wires is no go for 20A continuous.
Over discharge current protection could be simple 20A fuse.
Bms boards are not expensive neither heavy...
Wouldn't it be more simple to use ready made high discharge rate 2s battery pack with bms?
Good point regarding the 20amps going through the springs of the battery holder!
Had a rethink after all your advices and I'll go for an 11.1v protected lipo as sonofcy said, it'll make my life easier, just have to redesign the battery cradle of the robot.
I also realised, after some testing, that the DC motor for the BB gun didn't have enough torque at 7.4v, much better at 11.1v.