Is it safe for a woman during her fertility or ovulation periode and after a protected intercourse to avoid any possible pregnancy or does she need to take birth control pills?

Safe vs. Unsafe: "Safe" means different things to different people. A couple is safe from pregnancy if one effective pregnancy-prevention method is used... meaning only one effective method needs to be used. If the one method is not very effective at that moment, they can add a second effective method. A couple is NOT safe from transmitting infections to one-another unless condoms or other barriers are used.