1. Yes you can. It will work fine, especially if you only use new cells, but the BMS will be only the only thing to trust that the battery pack is fine.
If possible I would add this:
https://www.aliexpress.com/item/F00872-Low-Voltage-Buzzer-Alarm-Volt-Meter-Indicator-Checker-Dual-Speaker-1-8S-Lipo-Li-ion/32601463913.html?spm=2114.search0604.3.16.307a79c7Hn22uu&ws_ab_test=searchweb0_0,searchweb201602_5_10065_10068_204_10130_318_10547_10059_10884_10548_10887_10696_100031_10084_10083_10103_10618_452_10139_10307_532,searchweb201603_60,ppcSwitch_0&algo_expid=793efc28-492c-4a19-b797-c89a9d7ba0d6-2&algo_pvid=793efc28-492c-4a19-b797-c89a9d7ba0d6&priceBeautifyAB=0
Quite nice, and allows you to check the individual cells voltages, and if the BMS cuts off at the right voltage.
2. If I were you, I’d pick a 24V charger/laptop power supply, and wire a buck converter with adjustable CC/CV, and set it 16-16,4V for much higher cycle life, like this:
https://www.aliexpress.com/item/Lithium-Charger-Step-Down-Power-Supply-Module-5V-32V-to-0-8V-30V-5A-for-Mega/32399062651.html?spm=2114.search0604.3.2.1b903378AqrHu4&ws_ab_test=searchweb0_0,searchweb201602_5_10065_10068_204_10130_318_10547_10059_10884_10548_10887_10696_100031_10084_10083_10103_10618_452_10139_10307_532,searchweb201603_60,ppcSwitch_0&algo_expid=966020f0-156b-43c6-b4e0-32dc3a3f9a52-0&algo_pvid=966020f0-156b-43c6-b4e0-32dc3a3f9a52&priceBeautifyAB=0
It’s really nice. You can adjust the current so you can do a slow charge at 1A, a fast charge at 3A, and if you put a heatsink on it, super fast charge at 4A.