Building 3s 18650 battery pack
First of all it's a nice idea to recycle batteries from old laptop battery packs from an environmental point of view. Depending on your planned usage I wouldn't expect too much from these batteries as they might not hold their full capacity anymore or might be damaged in another way (higher ESR, weak chemistry, ...).
To answer your question(s) more precisely it would be good if you could clarify some things:

how does your powerbank circuit look like?
what is this 220 Ohm resistor about and why should it speed up charging?
what exactly do you have in mind?

I don't think there is a shortcut to analyze the (remaining) capacity of your cells rather than fully discharing and then charging them with a suitable charger. The iMAX B6 Charger would be an example (there might be cheaper ones but this is a good quality charger used a lot from RC hobbyists).
Regarding the protection you must differentiate between protecting a battery pack or protecting a single cell. I would highly recommend doing both as there is the possibility that a defective cell will short and this is a problem if you put batteries in parallel because the whole pack will fail then rather then tripping the protection of the single defective cell.
Please provide more information about your project like a sketch/schematic. Otherwise its hard to guess what you have in mind and where exactly you need help.