Should Ladies Wear Head Coverings in the Church? (A Genuine Question)

Some genuine questions from 1 Corinthians 11.  I would love to hear your thoughts...

1)  Chapter 11 teaches a woman is to wear a head covering when praying or prophesying.  What are we supposed to do with this?  Or perhaps a better question is - What is our rationale for not doing this?  This is NT stuff, after all.  Not OT.

2)  This is not the only instance of the NT associating ladies with prophesying, but what exactly does this mean, and what is the application to us?  What influence (if any) should this have on the typical Baptist position that ladies don't preach?

3)  What in the world does Paul mean in v10 when he says ladies ought to wear a head covering "because of the angels?"  Does that seem bizarre to anyone else?

Again, no agenda here.  Just asking questions.