(2) What Polk did with Oregon Country:
(a) Oregon Country
https://en.wikipedia.org/wiki/Oregon_Country
(view a map whose caption reads: "The Columbia River [note its presence] and its tributaries * * * ")

section 1 Toponym: "The term orejón comes from the historical chronicle Relación de la Alta y Baja California (1598)[6] which was written by the New Spaniard Rodrigo Motezuma and which made reference to the Columbia River when the Spanish explorers penetrated into the North American territory that became part of the Viceroyalty of New Spain [click for map only] * * *

section 5 Oregon Treaty: "In the 1844 US Presidential election, the Democrats had called for expansion into both areas. After being elected president, however, [Democrat] James K Polk supported the 49th parallel as a northern limit for US annexation in Oregon Country. Polk's uncompromising support for expansion into Texas and relative silence on the Oregon boundary dispute led to the phrase 'Fifty-Four Forty [or '54-40'] or Fight!' [the top map in this Wiki page shows '54 40' -- extreme US claim'/ there is a page in en.wikipedia.org for 'Continental Divide of the Americas'] referring to the northern border of the region * * *

(i) Spanish language capitalizes the first letters of proper nouns (person's name including nicknames, places from country down to village, but not languages themselves). So "orejón" can not be proper name.
(A) Spanish-English dictionary:
* orejón (adjective masculine; from [noun feminine] oreja [(outer) ear, as opposed to inner ear that one can not see)+‎ [suffix] -ón): "big-eared"
https://en.wiktionary.org/wiki/orej%C3%B3n
   ^ Spanish pronounced letter j same as English letter h, and words usually place accent on the second last syllable. Here the accent (or stress) is on the last syllable -- and hence the accent mark is necessary to indicate that fact
(B) Edwin Battistella, Oregon, the Name. Oregon Encyclopedia ('A project of Oregon Historical Society), undated
https://www.oregonencyclopedia.org/articles/oregon_the_name/
("The etymology of the name Oregon had been the subject of speculation during the nineteenth century, before the connection to Major [Robert] Rogers was understood. From present-day California to Vancouver Island in British Columbia, the Pacific Coast had been explored and colonized by the Spanish during the late eighteenth century. Some early theories were that the name Oregon had been adapted from either the herb oregano or orejon [sic; should be orejón], which means 'big ears' and was believed to have been used by Spanish explorers to refer to some Indigenous people")

This (Web) page described orejón as an "earlier theory" and propounded Robert Rogers as the one who initiated the word that is now Oregon, based on

TC [Thompson Coit] Elliott, The Origin of the Name Oregon. Oregon Historical Quarterly (quarterly of Oregon Historical Society), June 1921.
https://en.wikisource.org/wiki/O ... _of_the_Name_Oregon
(C) etymology of Oregon
https://en.wikipedia.org/wiki/Etymology_of_Oregon
enumerates and summarizes all proposals.
(ii) New Spaniard was a resident of New Spain.


(b)
(i) James K Polk
https://en.wikipedia.org/wiki/James_K._Polk

introduction: From Tennessee, Polk is "the only person to serve both as Speaker [of US House of Representatives] and US president. Polk left Congress to run for governor of Tennessee, winning in 1839 but losing in 1841 and 1843. He was a dark-horse candidate in the 1844 presidential election as the Democratic Party nominee; he entered his party's convention as a potential nominee for vice president but emerged as a compromise to head the ticket when no presidential candidate could gain the necessary two-thirds majority [in the party convention]. In the [1840] general election, Polk narrowly defeated Henry Clay of the Whig Party and pledged to serve only one term.

section Early life: "In January 1816 [age 20], Polk was admitted into the University of North Carolina at Chapel Hill [established Dec 11, 1789] as a second-semester sophomore. The Polk family had connections with the university, then a small school of about 80 students * * * After graduation ofrom the University], Polk returned to Nashville, Tennessee to study law under renowned trial attorney Felix Grundy

section 4 Presidency (1845–1849): Oregon Country
        You only browse section 4.2 Foreign policy, section 4.2.1 Partition of Oregon Country
(ii) However, to comprehend section 4.2.1, one needs basic knowledge (geography) of the following landmarks:
(A) Puget Sound
https://en.wikipedia.org/wiki/Puget_Sound
(section 1 Names)
• sound (geography)
https://en.wikipedia.org/wiki/Sound_(geography)
• sound (n): "1:         a: a long broad inlet of the ocean generally parallel to the coast
                        b: a long passage of water connecting two larger bodies (such as a sea with the ocean) or separating a mainland and an island"
https://www.merriam-webster.com/dictionary/sound

Long Island Sound of New York State fulfills both definitions.
(B) Salish Sea
https://en.wikipedia.org/wiki/Salish_Sea
(section 1 Name, section 1.1 Etymology: 1988 (named after Native Americans who had lived there) and composed of 3: Georgia Strait, Puget Sound, and Strait of Juan de Fuca)
Search images.google.com with this term (together with the word map) will show you (such as from Encyclopedia of Puget Sound AND SeaDoc Society) the extent of this term (3 arms: Georgia Strait extending northwest, Puget Sound extending south, and Strait of Juan de Fuca extending west -- from Victoria, BC or Bellingham, WA.
• Queen Charlotte Strait
https://en.m.wikipedia.org/wiki/Queen_Charlotte_Strait
(view the map with caption: "Queen Charlotte Strait is located southeast of Queen Charlotte Sound." Here, the latter fits definition 1 b of sound in Note (b)(ii)(A) above)
forms the northern boundary of Vancouver Island and connects to Georgia Strait.
(C) Fraser River
Search images.google.com with this term (together with the word map), and maps from Encyclopaedia Britannica and
File:FraserRiverBritishColumbia Location.png
https://en.m.wikipedia.org/wiki/ ... lumbia_Location.png
(the green area around the River is its watershed or drainage basin)
are helpful.