The max/min bounces setting determines the maximum and minimum of light bounces on a global scale and overwrites the setting for the individual types if they are outside of that range. If you have your minimum set to 5 and maximum to 10, and you have say the diffuse bounces set to 1, cycles will calculate 5 bounces. If diffuse is set to something within the min/max range like 7, it will calculate that exact ammount. If it is above, it will calculate 10.
Generally speaking, yes. More lightbounces tend to be more realistic, but can produce more noise and take longer to render. The reason for this is that cycles is a stochastic path tracer, meaning when it calculates a sample it uses a random variable to determine where and how it bounces off surfaces and how intense the luminosity is. If I am not mistaken when you use 0 bounces, it will hit for example a glossy surface and that’s it. There is little possible variation, and all samples/variables will be very similar/the same, therefore there is no noise. If were to use more lightbounces, a ray will hit the glossy surface, bounce off, hit a different surface, then another and another until the maximum number of bounces is reached, or the ray goes off into nowhere. All these bounces add more variables to the equation, meaning two different samples may vary strongly in luminosity. Therefore you need more samples in order to reach an average luminosity.
I usually set the light bounces to the full global illumination preset (minimum 3; maximum 128), because while it may not be the fastest, there is virtually no case where it is not enough, and for very simple scenes it doesn’t tend to increase render times significantly, because rays will be terminated once they go off without hitting a surface, so for a simple scene it might only calculate a maximum of 5-10 bounces.
Light bounces likely aren’t the main issue here. If you ask me, the hirarchy of settings I would adjust to clear up noise/fireflies is probably something like samples - filter glossy - clamping - caustics - bounces - denoising.