1) Be honest and tell her the truth. If she's insulted and choses not to be your friend after that, then that's her issue to deal with.
Just be kind about it and say "it's tough for my kids to be distracted when they are doing their homework. Anyway, I don't need to get into more detail, I know you understand"
2) your work is beautiful and I am sure she would love it and put it in a safe place
3) ewwww