Why is the language of the Basque so difficult to learn and master? What exactly is the origin of the Basque people?
I don’t know that Basque is inherently more difficult to learn than any other language. However, the Basque language is related to no other; as such, new speakers have no referents in grammar or vocabulary to ease the path the way, say, English speakers would approaching German, or French speakers Italian.
Best guess is the Basque are the relict population that preceded the Indo-European peoples invasion. Blood studies (Sforza-Cavilli, I think) show their genetic distinction from other Europeans.
There is an old Basque legend that when the devil wanted to play mischief on the Basque - and grab a few souls - he started by learning the language. Poor old Red gave up after working for years just learn yes and no (or seven words - depending on the version of the story).
Basque is so hard to learn because it’s akin to Japanese, Guarani or Swahili in that it’s completely different than the ‘easy’ Indoeuropean languages that surround it.