The 1910 Frankenstein isn't lost! You can watch the whole thing here:
If another person corrects you for calling the monster Frankenstein and says: "Frankenstein is not the monster, he's the doctor," you can correct that person right back, because in the book, Victor is not a doctor at all. He's a student of chemistry and does not get his doctorate.
The Adam thing is from the book, where the monster says to Frankenstein: "I ought to be thy Adam." (He talks a lot in the book.)
"Burgomasters" or "burgermeisters" still exist. In the English-speaking world, they're now called mayors.
Young Frankenstein arguably takes most of its plot and characters from Son of Frankenstein, which is also the first movie in which Frankenstein has an assistant named Igor, brilliantly played by Bela Lugosi.
They were so sure they wanted Lugosi for the role of the monster in the 1931 movie, they even had a poster made with his name on it. Though the artist didn't seem to know what Lugosi looked like, nor what the story of Frankenstein was about. Still an awesome poster.