Electronic – charge a the Li-Ion batteries using a regular power adaptor

Depends.

What do you want the BMS to do?

When I design a BMS, the first thing it does is safety:

• Temperature monitor for charge/discharge
• Over current events (with a software fuse)
• Charge control
• stopping over discharge events

The only other tasks a BMS will do are things like:

• state of charge
• some basic functionality (if you're doing something very basic, complicated functionality should be taken out of the BMS to make sure the safety tasks are taken care of)
• cell balancing (if you have a series pack of cells)

So, as you have your charger outside the BMS, the question is how safe do you want you pack to be? If you're selling it, then you need a BMS as safety is (should be) paramount. If it's just for you, you know what you're doing, and you can control the environment, charge and discharge patterns and all that, then there is no reason to have any BMS at all.

Personally, I'd say yes you do. But if I'm quickly throwing something together, I have been known to go without.

There are two reasons you need to be concerned about the number of parallel cells in your battery pack

a) The current cutoff threshhold when doing the final CV charge is dependent on the battery capacity, which is dependent on the number of parallel cells. You simply need to know the numbers, and program your charger correctly.

b) In the event of a failure of one cell, the other undamaged cells in parallel with it may discharge into the damaged one, prolonging and exacerbating any 'vent with flame' event, turning a mess into a catastrophe, turning a damaged battery into a damaged vehicle or building. I talk from experience, my brother lost an eBike and the van in which it was being charged, and would have damaged any adjacent vehicles as well but for being parked in a remote corner of the carpark.

You can mitigate this latter problem by connecting a fuse in series with (ideally) each cell, or at a minimum with each small group of parallel cells. The smaller the group of cells, the closer it can be fused to protect it.