I would now like to know if it is easily possible to update wordpress when I only have FTP-access and phpMyAdmin.
WordPress has automatic update feature, that will do its best to perform update without you having to upload new version manually. It is not perfect, but it is quite robust and works on most configurations.
If changes to database are required for new version, WordPress will perform them by itself, you won’t ever need to use phpMyAdmin for that.
I would also like to know if it is easily possible to make backups.
There are numerous backup plugins for WordPress available, both free and paid. They differ in what is backed up (files and/or database), backup destinations (local/email/cloud/etc) and additional features (restore/migration/whatever).
It will take some research to pick one for your needs (especially if you are looking among free solutions only), but this is definitely not a problem with WP.