Is there any way to do a 100% NANDROID backup without any warranty voiding?
Nandroid means using custom recovery (TWRP or CWM ) and in turn unlocking boot loader (on most devices). Whether this voids warranty or not depends on a) OEM b) Country / region specific laws. It depends on case by case so a general answer is not possible but in most branded devices it would void warranty
If there is a way to temporarily root or install TWRP, that would be fine too
Again depends on OEM and the Android version it is running. But by and large this is becoming increasingly difficult to do with OEMs and Android security features preventing this
Without rooting , if you wish to back up (not Nandroid) see this Full Backup of non-rooted devices