Samsung galaxy S4 mini : how do i backup original carrier firmware??? also OTA?

[AC Question]

I would like to make a backup of my custom EU carrier FW, which the carrier doesn´t have available to download from their site... so can i backup the FW that is currently in there and be able to restore it to FACTORY settings completely as it was when it was new? (same fw, same apps etc..)?
or
Is there some way to extract the OTA?
OR would it work to update to it after doing safe root that doesnt void warranty?

AS I DO NO WANT TO VOID the warranty...