> are hospitals referred to by name in any ballads that clearly do not have "Unfortunate Rake" related themes? For example any hospitals mentioned in war/wounded soldier ballads?

Great question. And the answer is No. At least none that's ever had any currency.

> Not exactly about leprosy, but a leper is important in the plot.

It isn't "about" leprosy in anything like the same way that the "Rake"/ "Bad Girl" is "about" syphilis. The "Rake"/ "Bad Girl" is almost explicitly a warning - as is, to a lesser degree, "The Streets of Laredo."

My point about plagiarism is more theoretical than legal. Students are warned against taking even a single sentence from somebody else's work without acknowledgment. (And taking too much even with it!) A student once asked me how altering a just a few lyrics or musical notes in a song in "the folk process" is ethically any different from plagiarism. Not a big question, obviously, but interesting in its own right for reflecting different views of artistic "ownership."