I'm trying to figure out if matinees (and the subsequent matinee prices) have always been a part of movie history or if they were adopted later on. I know matinee
was adopted by the English from the French in the 19th century to mean daytime (for daytime performance) (even though the French matinee means morning).
The first part of your question:
According to the Chicago Tribune:
According to Facts on File's Dictionary of the Theatre, the first matinee was in 1843, at New York's Olympic Theater. The same entry goes on to state that "they tend to attract audiences consisting of children and organized outings."
Couldn't find info on the history of matinee pricing. This book was mentioned in the linked article and might have an answer. It's viewable on a website, but it requires a research subscription. A lot of large research universities offer these resources to students free of charge, so someone else might be able to go check.
I'm not sure about the nickelodeon era, but I have a lot of vintage theater programs and advertising postcards in my collection. Here's an advertising postcard from October 1914 for the Knickerbocker Theater in Cleveland listing Wednesday and Saturday matinees.
Here is a vaudeville program from a Washington D.C. theater from 1907. There is a 25 cent matinee each day, and the final act is the American Vitagraph, a program of short films.