First question: Yes. The immune system releases pyrogenic cytokines such as IL-1. Bacteria aren't typically used to 37C, they prefer working at under that temperature to function in the environment. Our body however can take a few degrees here or there however this severely compromises the bacterial enzyme activity. The same is true for other pathogen enzymes. The body also increases copper concentrations in the blood for similar reasons. Problem is of course if the body goes into overdrive and raises our temperature too much, this compromises our own ability to fight the infection so in that case antipyretics like paracetamol can reduce fever.
Second question. It isn't a side effect, however paracetamol works by blocking things like IL-1 that raise temperature. How IL-1 raises your temperature is quite interesting, it tells the hypothalamus (our thermostat) that it should be set higher. So we feel cold (so we try to keep ourselves warm) and the body thinks it's cold (so it increases the temperature by burning glucose mainly)