Nope. The backup only needs to store the "user data" for each app and the rest of the backup will be your messages, etc. The apps themselves will download from the app store, music from Apple Music/iTunes, etc on a restore.
Use iTunes to store all music you acquire from various sources. That’ll do it.
Yes. iCloud can only store up to 5GB of photos assuming iCloud backup is not enabled, unless you pay $1 per month for 50GB tier.