Does food fetus is exposed to affect taste after birth?

Perhaps. If i understand you correctly, you are asking if maternal eating habits during pregnancy can affect the infant's subsequent food preferences. My answer would be a definite maybe - I am not aware of any serious studies looking at this possibility, but as a father of two I am pretty sure there is a link. Until studies are done, this may be another reason to stick to a healthy diet during pregnancy!
Doubtful. The fetus is not exposed directly to any food ingested by the mom. All of the nutrients are digested and absorbed by mom and delivered to the fetus via the placenta at the molecular level.