Laura and Almanzo started courting when she was 15 and he was 25. They actually married 3 years later when she was 18 and he 28.
Charles stubbornly refuses to let Laura get married before she is 18. Yet he allowed Mary to be engaged to John when she was only 13 and told them they could marry when Mary was 15. Also, Mary wasn't yet 16 when she met Adam (she turned 16 right when they moved to Winoka) and although the timing isn't clear, it appears that she married Adam around a year later which means she was likely around 17.
The real Laura Ingalls and Almanzo Wilder married when she was 18 and he was 28. The couple remained married for 64 years, until his death in 1949 at the age of 92. Laura passed away in 1957 at the age of 90.
Even though Laura had her teaching certificate, she still was going to school because she did not have a high school diploma and there real Laura did not complete it.
The scene when Nels runs up the stairs with Harriet screaming after she flushes the toilet is reused footage from before when he was first trying to install the indoor toilet and plumbing,