This is one of the most difficult verses in the whole New Testament. Especially the last four words 'because of the angels,' ridicule everyone. So don't expect to get an anwer to all your questions today :-)
It is far-fetched to seek a connection between this passage and the (also enigmatic) verses in Genesis 6:1-4. According to Tertullian women ought to have a head covering, because they otherwise cause (male fallen) angels to lust. Such ideas do not occur at Paul (or elsewhere in the New Testament.) This concept probably tells us more about Tertullian than it does about angels...
A better point of departure is to investigate other sayings about angels in the New Testament. A good start would be chapter 6 of this very same epistle. We can imagine that this letter was read in the congregation and that at the hearing of 'because of the angels' in chapter 11 one thought back to chapter 6.
Do you not know that we will judge angels? How much more the things of this life! (1 Corinthians 6:3 NIV)Indeed! If we (in the future) will be judging angels, then we (in this case the women) can also decide for ourselves what to do with little everyday things of life like hair style and head coverings.
Kate Bushnell also referred to Matthew 18:10 (NIV):
See that you do not look down on one of these little ones. For I tell you thatIn the context of this verse, Jesus puts a child in the midst of the disciples and taught them to become like a child. The idea of this verse is, that angels with a task that concerns us, stand before God without any kind of covering. If our ministering spirits (Hebrews 1:14) are allowed to see God face to face, then we also have the choice to approach God uncovered.
their angels in heaven always see the face of my Father in heaven.
So the conclusion is that, also in connection with the angels a woman can decide for herself how to dress herself (regarding her head.)
The original post in Dutch can be found here.