Can't save anything on mac

This one? Resolve issues caused by changing the permissions of items in your home folder - Apple Support.

Regardless of the problem Permissions outside of the Home folder lie beyond the user's ability to control. You may no longer, for example, save or alter anything at the root level of a macOS startup disk, because it is protected from alteration. If the app or program you are using was designed to save its information there, it requires an update from its developer.

Have a read of this https://appletoolbox.com/2016/07/fix-corrupt-user-accounts-macos/#Reset_Home_Fol der_Permissions

It talks about resetting home folder permissions and acl’s (about third of the way down), but for Sierra and High Sierra this apparently is no longer possible (or necessary) because the OS does this for you when updating itself!

So, I would try downloading the latest Combo Update and reinstall manually to see if it does in fact do the required “repair” as Apple now maintain.

Download macOS High Sierra 10.13.3 Combo Update

Obviously, as always BackUp any important data first.

The padlock locking has nothing to do with the problem. It should re-lock to prevent changes. It doesn't control access except to the settings that do.

If you've run this and still have problems, where are you trying to save documents?

Resolve issues caused by changing the permissions of items in your home folder - Apple Support