Great to hear you are using the Docker based installation of Xibo CMS, I will answer your questions in order:
You can check you database backups by going to the directory where you installed your CMS then looking in the shared/backup/db directory. You should find your latest Database backup here. You can then check the created date for that file to know when the last backup was made.
Essentially you will need to ensure you have a copy of the backup files in your shared/db and shared/cms directories. As long as you have copies of the contents of these directories, you can use them to restore your CMS.
Many Thanks.
As long as you have retained your Xibo config and compose files, along with the shared files mentioned above, you should have everything you need to restore your CMS. As long as you place those files in the correct directory locations for your installation, you should be able to docker-compose up -d your CMS again.