No, you actually have LESS of a chance to become pregnant then. Your most fertile days are approximately halfway through your menstrual cycle. The first day of your cycle is the first day of menstrual bleeding. Typically ovulation (fertile period) occurs approximately FOURTEEN days BEFORE the start of your period. Of course this may vary some from woman to woman.
If you ovulate less than 10 days before your period starts then it is extremely hard to become pregnant. It takes a few days after fertilization for the embryo to implant. Once implanted it takes another few days to produce a high enough level of HCG (thre pregnancy hormone) to alert your body that you are pregnant and therefore stop menstruation. If there is not enough time between ovulation and the start of bleeding the fertilized embryo will simply be flushed out with the rest of the endometrial tissue during bleeding.
It depends on when you ovulate. I do know a woman that ovulates 3 days before her period which actually makes it very hard for her to get pregnant. Every woman is different. You should track your cycles and find out for sure when you ovulate if you are trying to conceive.
No, you can only fall pregnant in your fertile period (when you ovulate) - that also depends from person to person, most women ovulate on the CD14.
No. Most women usually ovulate halfway between periods. So for example if you periods are every 28 days you would typically ovulate around day 14. Right before a period the cervical mucus has usually totally dried up. That is one of the best ways to see if you are fertile by seeing what your cervical mucus is like after your period ends, leading up to ovulation you should start to see more (check this when you wipe after going to the toilet) which goes from very little which is white and sticky in colour, then goes more cloudy and gets very stretchy (any time from this point is good to start trying to conceive) finally it ends up and egg white consistency which is the peak of ovulation.