May a probate administrator, after probate has ended, file a civil complaint against a party who damaged probate property?

No.  By closing the estate, the administrator ends his or her own authority, says, "my job is done."  The final accounting also necessarily says, by what it is, that all claims have been worked out completely.  Any claim like this would have to be filed and resolved, before a final accounting would be appropriate.

It may be possible, if there's a good reason why the damage wasn't something that the administrator could have known about when the estate was finalized, to re-open the case.  But if so, the application to do that needs to be filed immediately.