Hi! You’ve shown interest in a very different field and the good news is that this course can be undertaken and there is an engineering in music. It is called music/ vocal/ audio engineering. You can look for these courses in Mumbai music institute and few other institutes in mumbai, pune, delhi etc. Surf the internet to know more. Good Luck!
Yes there is such course but not much related to it.
The course is Instrumental Engineering or Instrumental and Control Engineering.In this course operation is done to analyse instruments and it's process.