Exchange 2010, 2013 and 2016 maximum mailbox size

That seems like a bad reason to remove the Administrator's mailbox. The yearly per-user pricing on ESET's Mail Security for Exchange is under $30 in blocks up to 5 users. It goes down as your numbers increase. How many users are you licensed for? Are you really that constrained?

Either way, to remove the administrator mailbox, something like this should work:

get-mailbox -id administrator | disable-mailbox

Note that for Restore-Mailbox you should be using the DisplayName as reported by

Get-MailboxStatistics -Database MYRECOVERYDB

as the parameter to -RecoveryMailbox. If the DisplayName contains spaces, you have to enclose it in quote signs ("Lost Mailbox").

The "MailboxDisabled" storage limit status should not prevent you from retrieving data off the mailbox, it just is a status set when mailbox storage limits are exceeded. If you are concerned by this, you should be able to change the limits by running Set-Mailbox with the -ProhibitSendQuota and ProhibitReceiveQuota parameters and waiting a bit (the information store caches this information and refreshes it every 2 hours, so it might take that long for your change to show).