Yes. First of all the entire country of greece seems to have no problems with eating feta and having babies. The issue with soft cheeses is not the cheese per se but that soft cheese may be made from unpasteurized milk and that can be linked to listeria infection. Most cheese in america is made from pasteurized dairy including feta. In addition, listeria can grow in any spoiled food, not just dairy.
Yes, if pasteurized. All pasteurized dairy products are safe in pregnancy, including my favorites - greek feta cheese and greek yogurt.
Yes. There is no contraindication.