My girlfriend took the pill a while ago but stopped because was having side effects. but now we want to start having sex and we want to know if we have to wait until she takes the pill and if yes, how much time?

A general rule is to use backup birth control for the first month after restarting the pill. It takes time to be sure the body adapts to the meds and that egg release will not occur. Some pill makers suggest two weeks is enough wait. If avoiding pregnancy is important, double coverage for a while would be prudent.

This depends on if you want her to become pregnant or not? You did not say. No birth control method gives a 100% protection. I would follow her local Drs recommendation as they will know the meds available over there that work the best in women like her who live where you live. Prob the most effective is for you get a vasectomy or for her to have her tubes tied.