Can my diet prevent allergies?

No. The studies to date are conflicting regarding maternal diet in pregnancy and later development of allergy in children, so no clear recommendations can be made at this time. Some of the most intriguing data, however, suggest low vitamin d levels may correlate with later allergic diseases such as asthma. So, taking a vitamin d supplement when pregnant may be worth discussing with your obstetrician.
No. No. There are many myths surrounding allergies, but many studies have looked at this issue and show quite conclusively that mom's diet doesn't affect junior's chance of getting allergies. Enjoy whatever foods you'd like.