Is there a way to lock/protect a kml/kmz file that is created in ArcMap from being copied in Google Earth and/or geoprocessed in ArcMap when you want to give to third parties?
KML is just XML. That is plain text as XML. KMZ is XML that has been zipped and could include other elements like images inside. There is nothing special about it. That's why so many software packages can read it / use it.
There is no mechanism within ArcGIS to "lock" or secure a KML/KMZ. Even if one existed, some other software package wouldnt care about the 'lock' and just read the XML data inside.
To my knowledge there is no way to secure a KMZ. There is some conversation here: https://productforums.google.com/forum/#!topic/maps/AHVe3PjBu5I - but it boils down to once someone has your KMZ, they have free access to whats inside.
You could possibly host your data as a service and make a KMZ that references that service. Odds are people could still put the geometry out of that (if they really wanted too), but it'd make it a tiny bit more difficult.
No. License restrictions are effectively an "honor code" issue. If you allow fair use, you can't prevent unfair use. If you don't trust the end-user(s), don't give them the data.
You could use the option to generate a licensed file geodatabase
Generates a license definition file (.licdef) that defines and restricts the display of contents in a file geodatabase. The contents of the licensed file geodatabase can be viewed by creating a license file (*.sdlic) and installing it with ArcGIS Administrator. The license file is created using the Generate File Geodatabase License tool.
Licensing is ideally suited to mature datasets that will be shared or licensed under a use agreement and do not require further editing. The output licensed file geodatabase cannot be unlicensed to return it to its original unlicensed format.