1. If you destroy the jukebox while a disc is playing it will continue to play until you reload the world.
If you use a hopper to insert a disc in the jukebox you can't play it
with a redstone signal until you either look in the jukebox or reload
I'm using the latest version of Forge for 1.7.10.
For number one, I will have a look into it, and for 2 interesting, though I can see why that happens, though I think I know a way around such an issue, though it might be a while for me to do it, as of recent I have not been doing much in terms of Minecraft modding.