Is it safe to take novolog flexpen while pregnant or breastfeeding?

Yes. Insulin is safe to take during pregnancy and breastfeeding. In fact, it is very important to have good control over your blood sugar. Your doctor will need to help find the correct dose as this may change during and after the pregnancy.
Yes. It is a category b drug. Problems in animal studies probably relate to high doses causing hypoglycemia. Talk to your high risk pregnancy team.