Using a lithium ion battery without BMS is not possible with safety. You can have one cell with overcharge protection. But 2 cell (7.4 V) or 3 cell (11.1 V) packs require a BMS to charge the battery fully without any problem.
Let's look at the facts:1. Each Lithium ion cells has a nominal voltage of 3.6V2. Your drill battery has 18V/3.6V = MATLAB>> 18/3.6ans = 5 cellsFYI, (5>1)3. Lithium batteries should not be charged without a BMS:4. The charged voltage of a 3.6V cell is about 4.3V5. The drill battery connector has one GND and 4 positive terminals.6. 4 * 4.3 = 17.2V
I don't know how to tell you this but you don't need a BMS if all the cells are in PARALLEL, for the OBVIOUS reason that they are SHORTED to EACH OTHER and therefore ALL CELLS will (MUST) have the SAME voltage. If you can figure out how it is possible for 3 cells shorted to each other to NOT have the SAME voltage I would certainly be curious to hear it.
I only answered part 2 of your question. I actually did not notice the 1s3p part of your first question. My bad. So, by accident, I just answered part 1 in my last post, somewhat belatedly...