If you chose to follow @grb’s advise, which I do recommend, first create an export of your vault in unencrypted JSON format and place it on a flash drive that is normally offline.
When they restore a 7 day old backup, you will lose anything created or updated in the past 6 days. JSON backups are as complete as you can get, and the unencrypted format is somewhat human readable. It may serve as a handy reference for bringing the restored vault back up to current.
Other than this one “special” situation, it is better to use password protected JSON export. Here is a good reference for creating reliable backups.
It should be. Free accounts are permitted to create one organization. Organizations are the raison d’etre for the amin console. That said, the lack of an admin console is not important right now. Recovering the missing data is much more time-sensitive. After that, get everything into a current backup.
Eventually restoring the admin console might require creating a new vault and importing the backup into it. Not difficult, but also would significantly complicate recovering the missing data in the old/current vault.