Bleeding is pregnancy can occur, yes, but is is NOT period and cannot be one.
A period is the shedding of womb lining/unfertilised egg from not being pregnant. You cannot have this if you are pregnant.
Yes it is not uncommen early in pegnancy especially or even During to have periods
No, if you are on your period that means you are not pregnant and you you're not in your fertile time to conceive either.