Would I need to wear dresses/skirt and cover my head at religious sites?
No shorts, short skirts, bermudas or bare shoulders.
No need to cover your head.
Sometimes at the entrance of churches or monasteries shawls or robes are available to cover you if necessary
For women visiting religious sites in Greece, it is recommended to dress modestly and cover their legs and shoulders. This typically means wearing clothing such as long skirts or dresses and shirts that cover the arms.
On Paris the church in main town had a rack of shawls you could borrow to cover what ever ( in my case I just needed to cover my shoulders as my skirt went to my knees anyways - but I saw others tie it around their waists if they were in shorts