Can a woman get pregnant under these conditions?

Whenever you have unprotected sex you run the risk of getting pregnant. However, if you had sex 3--4 days following your period your chances are slim. You do not ovulate until 11--21 days following the start of your period.

When starting birth control it can change your periods. Sometimes your period may be light or non-existant (depening on the brand of birth control). If you are ever concerned you can always take a pregnancy test to ease your mind.

Slim to none. Your period will be a little different after going on the pill. You'll need to get used to how your period acts again, but you sound fine. There is always a slight chance that something went wrong and you did get pregnant, and that the pill is not fully affective till the second month, but I'd say your chances of being pregnant are like 1%

of course you can get pregnant.

Honestly you could get pregnant even if you take your pills every day at the same time for a year; pill only has like a 95% success rate. I know that seems like a lot but what if you are in the 5%?

Good luck

Since you have to be on birth control for at least a month for your body to get used to it BEFORE you have unprotected sex, it is very possible...but since there was a period, it may just be your body adjusting to it, so I would say it would be fine.