You can have bleeding while pregnant. However, it is physically impossible to have a period while pregnant, as it sheds the lining of your uterus. If you had a period while pregnant, you would miscarry.
I bled my whole first trimester with my dd, but it was not a period.
generally no, once your period starts then you cannot be pregnant, having said that, its not uncommon to have a bleed around the time your period is due and be pregnant, the bleed will be different to your usual period though, it maybe lighter or shorter than whats normal for you