Technically no... semantics though. You CAN get pregnant from having sex on your period. But you cannot physically get pregnant while on your period, you can only 'become pregnant' when an egg is released. Not trying to be pedantic just as specific as possible haha

Yes you can. Sperm can survive in the vagina for about 5 days so if your cycle is like mine where your ovulation is almost directly after your period, then yes, it is possible