No, you cannot be pregnant if you did not have sex after the seventh day of your last periods. You cannot become pregnant if you have sex in the first seven days and last seven days of your periods. There may be some other reasons for late periods, like hormone imbalance, stress, etc;
Yes. It is possible that you became pregnant the previous month. Light bleeding or even what seems like a normal period is not unheard of in early pregnancy. This is sometimes known as implantation bleeding. A pregnancy test should give accurate results at this time.
No. Many women are late with their periods, and that doesn't mean they are pregnant, but you definitely aren't pregnant if you haven't had sex in the month, as that is mandatory!