Hi Sweet Desert
I like your user name. I had to look it up to see if it was what you eat at the end of a meal or the "barren land" as I can never remember which is which. I digress...
There are absolutely no references to "nuns" in the bible, including the new testament. In the 76 books that make up the "Testaments" (different versions may have more or less, and of course the Jewish faith does not have the New Testament), only two have a women's name as a title: Ruth and Esther. These are found in the Old Testament, which means they are of the Jewish faith (and this has been intergrated in the christian faiths). No nuns in Judaism. Having been exposed to the christian faith, I have only a vague notion of other religions, practices, or beliefs. Your question(s) do refer to the bible.
It is, I would want to say, a-b-s-o-l-u-t-e-l-y impossible to have a complete awareness of, mmm, History. All that has transpired throughout the years to influence, change what occured, and what was retained of that, how it was explained, described; and how it is told x number of years later. "Nuns" would have started sometime in the 4th century after Constantinople made a "political" decision to convert to catholicism. Nuns did not exist, ever, before that. I have no idea how nuns came about to wearing "veils", whatever form they have, and still do someplaces, take. I can say that following Vatican II (1962-1965), nuns started to "unveil" and "dress normal" here in Canada.
I would suggest that the veil, and the uniform since some congregations had an attire that was black and covered the whole body, some covered the face as well and only permitted the wearer the possibility of seeing the floor, were for notions of humility and piety. You see this with Franciscans (way back, not so far when!) where the hands are drawn inside the sleeves, the head is bent forward and the hood falls over the face, which you cannot see. Further "veiling", if you will, was being "cloistered". You never get to see the outside world, or they, you... and they remain fully covered within the cloister. Part of it, too, would be to hide your "sex appeal" and discourage "attraction". The "cloistered" would want to limit all stimuli so as to devote their every moment to communing with God.
Life in this country -Canada- has changed considerably in very recent years. I struggle with my identity in this land that forces me to review my living, and very recent history. I am in a country that was never what it is now till I was past 30 years old. I believe strongly in freedom even if I know that my awareness of what "freedom" is is limited.
9-11 has become a reference point, in my social consciousness, that justifies establishing a limit on a "dress code". I respect your (whoever) personnal beliefs, but if they compromise our common sense of security, in any way, then, I would vote for an acceptable "public" dress code which would set limits on how you dress when outside your personnal environement. Security then compromises freedom. And "religious practices" would be quartered to a more personal environement.