Why in ''Little house on the prairies'' some characters have accents that would be considered foreign nowadays, similar to someone who learned English as a second language.

There was a big boom in migration to Kansas about the time the Ingalls arrived, mostly prompted by the railroad. The Atchison, Topeka, and Santa Fe was completed in 1869, and the Kansas Pacific a year later. The population grew about ten fold in the two decades following the Civil War. There were large groups of German and Swedish immigrants, and an influx of Mennonites from the Russian Empire, who would have spoken German or maybe Dutch. These were descendants of the people who were invited to help populate the Volga and Black Sea regions after the conquest of those regions under Catherine the Great. Fortunately for Kansas, the Mennonites brought a variety of wheat called Turkey Red with them. Growing conditions in Kansas being not too unlike the Ukraine, that strain of wheat grew much better than what the existing farmers had been growing. Which is why Kansas is the #1 wheat producing state.

So, in Kansas in the 1870's, it would have been very common for people to speak with a German or Swedish accent, among others. German language newspapers were common up until World War I, and some lasted until 1941. Here is a good essay on the German immigrants to Kansas.