When is the safest time for copulation without getting pregnant if you are not using any birth control method ?

None. No safest time. If you don't want to get pregnant, abstain or use birth control.

WHY? Look at a large enough random group of women that have children... and you wiill find women in it that have gotten pregnant during every day of a cycle including their period.

And quite a few of them that got pregnant while using birth control.

You don't have unprotected sex unless you WANT to become a parent as a result. It really IS that simple.

There really is not. You can pick times that have lower chance.

There are many good forms of birth control.