Mine were there about the same time, and no, they didn't expect the Indians to teach them their language(s). They expected to speak English, and some of the Indians already spoke English when the Mayflower arrived. They had already picked it up English fishermen who had been visiting the coast for many years.
The original colonists were very dependent upon the Indians for their survival. In fact, they were so short of food that they stole corn caches from the Indians. They had found the caches as they searched around for a place to settle, and for food. The Indians had gone inland for the winter, and most of the Indian population had died off in epidemics over the previous few years. The Indians taught the settlers how to plant the corn, sowing it when a particular herring species came upstream to spawn.
It seems to work in the rest of the world. There are thousands of Palestinians born every year in the middle east, and they are still Palestinians.
I think that the UN should be buttessing costs against and collecting money from the countries that people are escaping from and then paying that money to the countries that are accepting the refugees. And FWIW.... Canada and the US are not the only countries where you find refugees. We actually get only a small number of them.