You most certainly can get pregnant a few days before your period. When you ovulate and nothing fertilizes the egg, that's what causes a period. I would take a pregnancy test to be sure.
There is no "safe" time in your menstrual cycle. After all, your cycle naturally varies a little from month to month, which would result in changes of your fertile times.
This is a common misconception, because there is no safe time during your cycle. Believe it or not, you can even get pregnant (rare, but true) having sex during your period, so don't count on certain days to prevent pregnancy; get more reliable forms of birth control and protection for yourself.
Yes you can. No time is a safe time. It's possible to get pregnant at anytime in your cycle. Don't believe the myths. If you do not want to get pregnant then you should use proper precautions.