Charging DIY bluetooth speaker

Hello, i am buildng a DIY budget bluetooth speaker. On the picture you can see the layout. 5 batteries in series, BMS protection, batteries connected to either amplifier or to charger (when i use speaker, batteries are connected to amp, when i want to charge the batteries, there is connection between batteries and 21V DC).
I have a few questions, keep in mind i want to keep this as simple and cheap as possible.

1) As you can see i want to charge batteries in series. I dont have a special charger for that, but want to just connect batteries to 21V. Will that protection board be enough to protect the batteries ? It is overcharge/overdischarge/overcurrent 5S protection BMS board. When i assemble it all, i will test whether during charging any cell goes above 4.2V. In theory, it shouldnt, right ?

2) Anything else i should change or should this, at least in theory work ?

You can’t just hook the battery to a DC 21V supply, you’ll need a charger.

Ok, are there any cheap chargers for 5 batteries in series ? I dont want the charger to cost more then everything else

Could you use a 4S1P/4S2P battery pack instead?

Using a 4S battery pack would allow you to use a buck CC/CV converter that will charger the battery pack adequately.

Well i guess i could, though this amplifier is supposed to work better with higher voltage. Could you maybe give me ebay/alibaba link to the charger ?

What if i just use a cheap charger for 1 cell from ebay and just charge each cell individualy, even though they are connected in series ?