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To answer question 1, "Is it a belief of the Mormon church that a curse from God is the initial origin of all dark skin among humankind today?", we have, from lds.org:
Today, the Church disavows the theories advanced in the past that black skin is a sign of divine disfavor or curse, or that it reflects unrighteous actions in a premortal life; that mixed-race marriages are a sin; or that blacks or people of any other race or ethnicity are inferior in any way to anyone else. Church leaders today unequivocally condemn all racism, past and present, in any form.
Or, more concisely, no, that is not an accepted belief of the LDS Church.
Question 2 seems to be based on a "yes" to question 1, so I don't have a good answer; it does appear that a "skin of blackness" was placed on the cursed Lamanites to make them less appealing, as you quote from the Book of Mormon, but that was a localized instance, rather than something generalizable to all people with darker skin.
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Is it a belief of the Mormon church that a curse from God is the initial origin of all dark skin among humankind today?
Some believe this, but it is not a teaching of our scriptures. The Curse is the separation from God due to sin.
Blackness is a Hebrew idiom for gloom/sinful.
White is a symbol of purity and salvation.
The skin is the covering of the body. So just like a hard heart, or blind eyes or a "stiff neck" are easy idioms to understand, so should "black skin;" it just means sinful person, so sinful that they are covered in sin.
No person on earth is literally black or white. Everyone is a shade of brown from the lightest shades in Norway, to the darkest shades of brown in Africa and Asia.
Did God choose black skin in order to make the cursed people unappealing (as it seems to say in 2 Nephi 5:21)?
No. None of them changed colors or were given a literal dark skin color by God. In fact later it explains the Mark. The Mark was in Alma 3 - It says they placed Red on their foreheads like the Lamanites, and that they didn't shorn their hair like the Lamanites though.
There was zero color changing in the Book of Mormon.
Curses are by choice of leaving God and his Church. Marks are self applied to separate and differentiate what culture you adopted e.g. Nephite or Lamanite.
All references to Skin color are metaphor, unless specifically referring to skins worn as a Loin cloth by Lamanties / Gadianton Robbers.