You can't have permanent exceptions in PB mode like page zoom that last across a session. In PB mode all session data is kept in memory and not stored in the profile folder, so any website releated changes you make are lost apart from bookmarked pages.

I'd like to ask if Firefox does not have anything to do with remembering the specific website zoom settings & no add-on is not the reason why, what could it possibly be? I like using PB most of the time. Thank you

Site-specific preferences (like zoom levels and popup permission) are not written to a settings file in private browsing because that would build a list of sites you visited, and the main point of private browsing is not to keep any history on disk.

I don't know whether there are any add-ons to store zoom levels (separately from Firefox's settings files) and apply them in private windows.

I have an update- I cleared the browser cache & cookies & then the startup cache in private browing using my Windows administrator account. I then closed & reopened Firefox using PB. I am now, for several days been able to get into most of my websites that "remembered" the individual site zoom settings. Could this be a bug in Firefox? I am told that it is impossible for this to happen unless there is an add-on to do this. I do not have such an add-on unless it is hidden.

Site-specific zoom levels created in normal windows carry over to private windows but not vice versa.

Private browsing mode (aka "Never remember history") only remembers site-specific zoom levels created before switching to private mode.