If a pregnant woman catches the flu is it possible to pass the virus into her unborn child?

No. Viral flu can be harmful to a pregnant mother but the baby will not acquire the flu virus. It is very important for all pregnant women to receive the flu vaccine when it is available before flu season arrives.
Hard to say. We know well that any virus that enters the blood (like flu) can pass to baby. How this affects baby is hard to say. Moms with a minor case will recover and may never have known they had flu. But some will have it so bad they die during pregnancy.An exposed fetus is not available for study during the pregnancy.
Media coverage was. given to one study from Denmark that showed a 3-fold increase in Autistic Spectrum Disorder in offspring of women who had the "flu" with fever for a week during pregnancy. No follow-up studies are available yet., but it is prudent to get a flu vaccine at least 2 months before conception or a flu shot, not the intranasal live virus, in the 2nd trimester if unprotected. .