Answer:
Option C “She, like many other composers in the 19th Century, died of syphilis”.
Explanation:
Statement C is false because while on a rehearsal in Berlin, she died of a sudden stroke, passing away at the age of 42 years old.
All other sentences are true: Both she and her brother Felix were great musicians (sentence A), Her family was a prominent member of the German society and thus she got cultural and musical private lessons with well known proffesionals (sentence B), Fanny gave private concerts at her home given that at that time was not well seen for a woman to be part of such public activities (option D).