Setting Up New iPad

You can selectively download apps that you have purchased in the past using the same Apple ID that you used to make the purchases.

Redownload apps, music, movies, TV shows, and books - Apple Support

What you cannot do is selectively download data for each app from a backup. However, if you were syncing content and files with iCloud, you can download those same files and content again by turning on the appropriate switches in the iCloud settings. Files and content like Notes, reminders, contacts, are not stored in the backup if you are syncing that content with iCloud.

No, You can make a backup from old device then do a restore from backup on the new device.

Once finished, you can delete what you don't want on the new device.

You're welcome.