I'm afraid I don't have answer for you, I'm not that familiar with BMSes, how they work and if you can trust the Chinese 50 pence boards with a Lithium Ion.
I also gather that advice on Lithium charging and tinkering tends to be quite light in here. I am wondering if that is more to do with the safety aspects around them, which are very often over stated and people not wanting to give advise in case the person explodes a LiPo on themselves and the person giving advice might feel responsible.
On BMS stuff, I'm curious to know more about them. I know quite a bit about LiPos and their charging etc, but not for hardware based electronics projects. I would be more interested in building a balancing LiPo charger than buying a BMS. But that's just nerd-ish-ness.
If you can find a few BMSes from a reputable brand which have datasheets and study them you might answer your questions.