How can I upload files to my Magento instance

You will need to use SFTP with key-based authentication.

You can add the key then configure your integration to connect to the adminssh endpoint using SFTP.

How can I connect to Magento's database server

There is no direct access to the database server from outside the Fleet environment.

You will need to set up an SSH tunnel between the service attempting to connect to the database and the database.