Why are we recommended to have at least 8 characters, and not 6 or 7 etc.? and the different set of character?. I only know that the longer the password is, the harder it is for brute force attack to take place. But why specifically 8 characters
You're right to state that password length recommendation is usually directly related to how hard it is to bruteforce attack it. When you combine this with the understanding that sophistication of attacks as well as computing power are increasing, it should follow that at some point in the past, based on computing power available, 8 characters was the "right" recommendation, and prior to this it could have been 6 or 7. Neither are the right recommendation today.
As computing power increases and sophistication of attacks increases, recommended password lengths will increase as well, to a point where it isn't feasible to use passwords which are any longer.