You recive points only if you kill units from your oponents if you kill other units stationated in the oponent castle but not from your oponent league you dont recive brawl points.

Hello. We attacked the trading post at the same time, and three attacks were successful, but the fourth attack arrived late at night. As a result, we did not receive any points in the Battle Arena. I would like to know if this will always be the case in the Battle Arena, and if it is better to stay inside the castle.

For example, we are against each other in a brawl, you attack my castle and kill troops, but you do not receive brawl points because the troops that are in my castle are neither mine nor any member of the league, but are defense sent from outside the league.

This was the case here, either it was defense from outside the league or the player was kicked out before your attack arrived a few seconds ago, that's why he still appeared as part of the league.