If you designate a static item or NPC with mark for delete (using the cheat console in game), will doing so automatically remove all resources/references to that object/NPC character in CK? What about the Data game folder if scripts for the NPC or object exist etc?

Or do you have to go into CK and manually delete the object or NPC character references?

Is the former the case? i.e. permanent object deletion, saving result in a new fresh save, exist and reloading that save?

Mark for Delete can only really delete objects that are dynamically created by the game. It simply keeps that item from being saved in the savegame file. Anything placed in in the CK isn't really deleted, but gets a "deleted" flag added to the savegame file instead so that that game will ignore that item in the future.

And you really should not ever delete anything through the CK that might already be used in a game. If you're updating a mod just mark the item as disabled and/or move it to an inaccessible location.
One of the "dirty mod" characteristics is trying to delete an object from the game world that was placed there by Skyrim.esm or some other mod. The most important stage of "cleaning" mods with TES5Edit is the process of undeleting anything that modders deleted in the CK and marking them as disabled instead.