Why are musical instruments forbidden on Shabbat?

Sorry to ask so many questions!

I can understand not wanting instruments during the service because maybe it’s distracting, but why is it strictly not allowed in itself for fun (or is it)? I read it’s because one might accidentally fix the instrument, but I do not know what this means or how this could happen (I play the piano and do not know how I would fix it accidentally). Alternatively, I heard it constitutes creative work, but which of the 39 melachot does playing music pertain to specifically then?.

Similarly, is dancing and/or clapping forbidden? I heard some say it is for the same reason as the instruments, but that makes even less sense to me. How does dancing cause one to fix instruments? If I am sure not to fix anything, can I play music and/or dance and/or clap? BTW, people clap at my synagogue (Chabad). What’s up with that?

Is there consensus on these issues (traditionally speaking)?

Thanks!