Can fibroids cause infertility?

Yes. Yes, especially if they are very large growing inside of the uterine wall, or growing in the endometrial lining. Surgical removal is usually quite successful. Remember though only 10-15% of all fibroids cause infertility.
Yes. Fibroids can definitely affect pregnancy rates. Fibroids that are submucosal (into the area where a pregnancy would implant) seem to decrease pregnancy rates and increase miscarriage rates. Fibroids that are in the muscle only seem to decrease pregnancy rates by a smaller amount. But usually fibroids are not bad enough to completely prevent pregnancy.
Yes . Depending on the location of fibroids in the uterus, they may interfere with pregnancy. Ask your gyn for a sonohysterogram which will show if the fibroids are inside the uterine cavity where they are most likely to interfere with fertility.