A: No. Women are free to wear a head covering to church if they so desire. It’s just not required.
The document Inter Insigniores by the Congregation for the Doctrine of the Faith (October 15, 1976) stated that the 1917 Code of Canon Law (canon 1262.2) requiring women to wear veils on their heads was a custom of the period and that such ordinances "concern scarcely more than disciplinary practices of minor importance." Thus the obligation "no longer has a normative value." But, as a sign of respect, women still are required to wear a veil when meeting the pope.