Well that's where you're wrong. As you know, Russia's defeat by the British Empire during the Crimean War led directly to its decision to sell Alaska. What you dont know is the thinking behind it. The basic thought was that if the Russian and British Empires went to war again, which seemed likely at the time (the rivalry you mentioned), then Russia feared that the British settlers in British Columbia would invade and annex Russian Alaska, which was far less populated and fortified. To cut its losses, Russia initially approached Great Britain with an offer to sell Alaska for a reasonably low price, so that if war did break out again Russia wouldnt lose Alaska without proper payment. Great Britain showed no interest in purchasing Alaska because they already had warm water ports in British Columbia and Vancouver. After that failure, the Russian Empire approached the USA with a slightly higher price than they offered the British. The Russians hoped that Great Britain would fear the possibility of British Columbia being surrounded by, or even annexed to, American territory, which is exactly why the USA wanted to purchase Alaska in the first place. Russia hoped that by offering to sell Alaska to the USA, Great Britain would offer a higher price to avoid letting the USA purchase it, and maybe even start a bidding war between America and Great Britain. Instead, Great Britain displayed little concern and the USA purchased Alaska for its low price shortly after the end of the Civil War.
In this timeline, because Texas is never annexed, the USA acquires more land in mainland British Columbia/Oregon and Great Britain shows more concern for the west coast of British North America, especially as American influence in the Crown Colony of Vancouver Island increases drastically with the start of the Fraser Gold Rush. When Russia offers to sell Alaska, Great Britain quickly accepts to prevent the USA from purchasing it and to take control of more Pacific ports.
Well you should blame the British government of the 1860s for that then. When Alaska was purchased, most of the country thought it was a major waste of money. I dont think that gold was discovered any earlier than OTL.
Texas is recognized by the Netherlands, France, and Belgium before 1845. It acquired loans from Netherlands and France to start paying off its debts, but those debts were considerably lower than OTL because Sam Houston was able to convince Lamar and the Texan people that peace and cooperation with the Camanche was the best policy that Texas could have. After 1845, Great Britain and many other countries recognized Texas, and Im sure it took out some lones.
While Texas and Great Britain's relationship is peaceful, it is a bit strenuous because of its alliance with Central America, which refuses to relinquish control of British Honduras and the Moskito Coast and threatens to expand its influence into the British West Indies, which become part of Canada in the 1880s to avoid foriegn occupation.
Well the Mexican-American War happened as a direct result of the US annexation of Texas, which claimed the Rio Grande as its southern border. The annexation of the Mexican territories of Alta California and Nuevo Mejico happened only as a result of the annexation of Texas, which was fueled by "Manifest Destiny" and irridentism. Without Texas being annexed, the USA would have no excuse to send troops to Sonomo, Alta California to convince them to revolt like they did OTL.
It could be argued that the USA would still try to create unrest in Alta California so that it could annex the territory, but it doesnt make as much sense because the USA and Mexico are not enemies in this timeline, so it would have no justification for war. Texas, on the other hand, was at war with Mexico, openly proclaimed its intentions to spread its borders to the Pacific Ocean, and was sending missions westward to try and convince America settlers to revolt and join Texas OTL
Are you talking about the Triple Alliance: Germany, A-H, and Italy? Because that seems pretty obvious.
The general pattern when it comes to American-British boundary disputes is that Great Britain has the power to back up its claims, but the USA has the stubborness, and the outcome is that the USA almost always recieves about 2/3 of the disputed land. Take Maine, Alaska, & Minnesota as examples. Oregon is one of the rare cases where the USA settled for 50/50, only because the Texas annexation and Mexican-American War required more of its attention.
In this timeline, Polk can concentrate all of his efforts on the Oregon dispute, and as always, to avoid war with Great Britain he settles for less than all of the claimed territory, but instead of splitting it 50/50 like OTL, he manages to gain about 2/3 of the Oregon Country, leaving Vancouver Island and the northern 1/4 of the Columbia District to the British. So you see, the compromise was just following a previously set pattern.
Are you asking that because you think in this timeline Great Britain and the USA are enemies? Or are you asking that as a completely separate question unrelated to this timeline?