Why was the texas annexation so controversial? what would have happened had texas remained an independent nation?

Backing in the history, Texas could be remained an independent nation by different situations. First, If Henry Clay had won the election instead of James Polk, Texas would remain independent for at least 4 more years, and Clay would run the party program around the "American system," a program designed to unify all portions of the country through the economic policies outlined by Alexander Hamilton in his Manufacturing Report. Second, If Texas simply does not join the Union, this could be because of Americans fear of war with Mexico or Texas nationalists continue hold power and refuse to join the U.S.. In this scenario Nationalists keep power in Texas and it simply does not negotiate, if this happened it would be very doubtful the Texan Republic would  have survived. Texas was never meant to be an independent nation, it was too under populated and largely rural. Third, If the Republic of Texas was controlled by nationalists it would either collapse under its own debt become absorbed by the U.S. or Mexico or be a weak country surrounded by 2 powers. This way, if we assumed if the Republic of Texas remained independent, probably Mexico would threat war, Britain would try preventing westward expansion, Mexico would preach Americans despoil it of Texas, Mexico would not recognize Texas’ independence. On the other hand, Democrats would be pro-expansion, the Popular idea would be in the south, not the north, and Texas would remain an independent nation would not have brought the U.S. into a series of wars.

the option which was not a function of missionaries in the northwest was the first one - they established posts for trading furs and other goods.

missionaries were sent around the world to spread religion and their knowledge and others - they were not merchants who sold furs and other goods.

france,russia and prussia had absolute monarchy and it meant:

when louis xiv inherited the throne, he was able to serve as his chief minister.louis xiv ruled as an absolute monarch.