How to connect four 18650 batteries to double voltage and capacity
That series-parallel arrangment is legal but could give some issue since cells will not be discharged in the same way. It will works but you'll have less than 4 times the capacity, probably.
Usually is preferrable to put all the cells in series and step down from the resulting voltage with a converter; even in that case there are cell balancing issues at some point (and dedicated ICs to resolve them!)
As for the battery protector: each pack must have its one, they are not designed to protect multiple packs (unless they are redesigned accordingly). You do not want a lithium fire on the bench, I assure you.