For the singing at mealtimes, have you considered playing music in the background? People could talk over it, but I'd think that singing a different tune over it would be hard.
For the interrupting, that impulse doesn't seem to ever go away, but most of the time, my DS stops when I hold my finger up. He knows it's an acknowledgment that his turn will come when I'm done--he doesn't need to guess when that is. I will address him when I'm finished with the current conversation. It doesn't stop the initial interruption, but it shortens the length.