Don't "Pass Though Charge." - There are some that allow this. I just grabbed one that does not because I needed one quickly and did not want to order one. Amazon has a few that work well for this.
Mosfet is not used to regulate power, it is like a switch and allows power to flow in one direction, it acts like a gate. The reason these may blow is because they are limited on how much current can flow across one. So if you are charging the pack and charging your phone it may be more current draw then it can handle.
Yes you are correct that a lot of these chargers lie on how much power they hold. Some manufactures round up while others test with fresh batteries in ideal temperatures. The higher temperature the shorter life you can expect from these batteries. I believe below freezing they will not charge at all but I am not sure on this one.
Edit: one other thing some manufactures lie or mislead people on is the charger rate. Some list one port as being 2A and another being 1A this is the current rating and how quickly energy can flow. Some power banks will provide this power, other will only provide 2A (2 amps) while only one port is in use and other will not provide this at all. Keep in mind that this will also be device limited. If your device can only charge at 1.5A and you plug it into a 2A port you will be limited to 1.5A. Some "smart" Chargers will limit you further. I have seen one that is rated for 2a but if you draw below 1.8A it drops you down to 0.7A thinking that your device is not able to draw more power then this.
Edit 2: here is a device that allows "Pass through" Charging https://www.amazon.com/MoKo-9000mAh-Portable-Simultaneously-Charge-discharge/dp/B00FGN1OBU/ref=cm_cr_dp_asin_lnk
I would actually redirect y'all to the Moko 10,000 mAh battery, which is the same price as the Amazon one. Only one real difference:
The Moko has pass-through charging, so you can charge your phone and bike light while charging the battery itself, either from an outlet or (if you're doin' it) a solar panel or dynamo hub. The Amazon one does NOT have this feature, so when you plug the Amazon battery in and then plug your phone on, too, it stops charging the Amazon battery.