Of course. If you were sitting in a courtroom and had to appear before your peers, you'd be on your best behaviour. We should always strive to be on our best behavior because we are always being watched.
If this were not the only command that was specifically said "because of the angels", you'd have a point.
no of course not. Its about respect for the headship arrangement that God has put in place.
Woman should not try to take the place of men in the congregation. Men have been set as the leaders and women should respect that role because Gods wants men to be in that role. He wants women to submit to that leadership.
In this case, men would also need to uncover their heads "because of the angels".
And I'm assuming you don't believe that the cover of the heads is the hair for the men as well right? Surely we aren't being asked to go skinhead every time we pray.