Hi Arthur,
From your description, it appears that an update may have failed partway, leaving the plugin in a broken state.
When attempting to install manually via FTP, make sure that unzipping the plugin file does not add an extra directory level.
When installed on the server, you should see the following structure:
wp-content/plugins/updraftplus/updraftplus.php
The plugin files should be in the wp-content/plugins/updraftplus
folder directly.
The installation failed error that you are seeing in WP Admin is often the result of a security module on the server cutting the connection early, before the installation process can complete. Your hosts would need to confirm if this is the case here.
Best Wishes,
David N