Normally it wouldn't be the most fertile time BUT each woman is different. I know for a fact one of my children was conceived the day my period stopped AND I was on the pill. It was the only day we didn't also use a condom and the only day we had sex as hubby left the very next day for a month long trip. So, it can happen, nothing is 100% effective unless you're 100% not having sex.
I'd say it's very possible. I know that when me and d/h were ttc I started using those little fertility tests...well the only time they showed i was fertile was DURING my period. So everyone is different and as other poster says there is always a chance of getting prego if you have unprotected sex.
Pretty much all home pregnancy tests...but i'd suggest waiting until the day she's supposed to start her period. There are the early pg tests...but since the concentration of pregnancy hormones is usually pretty low before your first missed period they aren't as accurate...in fact the directions even tell you that the accuracy continues to go up everyday closer to the day your supposed to have your period.
The closest to her ovulation you are, the bigger chance you have of getting pregnant. Ovulation is different for every woman, but it is usually 14 days after the first day of her period, so figure, she was maybe 7 days away from it.