When Paul talks about covering the head, does he talk of all females, or only of married women?

It would seem that he is referring to all women. He uses the illustration of husband and wife to show that the man had the greater responsibility and was head of his family. (See 1 Corintians 11:2-16.)

However, the woman was not inferior to the man in God's sight. What Paul says in verses 2-16 is because of the society in which they lived. Corinth at that time was a very sinful city and women who had no covering on their heads, were known to be immoral. Paul did not want the Christian women to appear like them. He wanted them to be seen to be different. A woman wearing a veil was respected, whereas, without a veil she could be insulted by anyone. It was a principle Paul was concerned about here. He wanted the Christians to be respected and seen to be behaving well and respectfully even when they were worshipping.

The same principle applies today. Christians must be seen to be reverent before God and behave themselves well. It does not mean that in places where customs are different and in all different times women should wear hats, but they should be seen to be following their Saviour and Lord.