Yes. You can even get pregnant during your period, though it is rare. Most women ovulate about 14 days before the start of their period...but sometimes a a woman will have a weird cycle and ovulate at another time...or even ovulate more than once.
I recommend using a condom (at minimum) anytime you have intercourse (until you are in a completely monogamous relationship and WANT to get pregnant)...as an unwanted pregnancy is the least of your worries given the number and variety of sexually transmitted diseases out there.
Yes, and you can get pregnant while you are ON your period too. Most people think if they're on it they're in the clear, not true!!!