Family Sharing

A couple things to note:

• You would need the Family subscription to Apple Music which is a little more to share with others even if using Family Sharing.
• Songs downloaded and playlists created using the Apple Music subscription will be removed when the service is cancelled. This is not the same as buying the song, which is done in the iTunes Store.
• She would still have access to any song that she purchased through the iTunes Store.

Yes.

Note that you say "bought". If this is indeed purchased music she can (in theory) always have access to it.

If this is subscription music then it requires a continuous subscription to ensure no loss, but that applies in the scenario you describe so she is okay.