Sorry, I did miss "edit2".
A "freeze" is a fatal error just like a "CTD", but it usually indicates that the next instruction code is not known and the OS can't pick it up and "handle" the error in a controlled manner with a "CTD". Checking the Eventlog is a forlorn hope that it contains a clue. Sometimes it pays off. Other errors listed may contribute to the problem. (Ideally you shouldn't have any errors in the log.)
When the "freeze" occurs in the main menu of the game, but before you have either started a new game or loaded a saved game, then it's usually due to a "missing" requirement or "master file". That might be due to a "master file" not being present, or in the wrong "sort order".
If the game can't even launch, then you are either pointing to the wrong location for it, or are missing something the game requires before it even gets to the point of loading plugins. (That is usually where the DX9, ".Net" libraries, and game INI files fail to be found.)
When you say "I deleted everything", did you "uninstall" the game from the Windows "Control Panel"? That is necessary so it properly removes registry entries. If not, then you likely have mixed values there which are confusing things. Just "nuking" files doesn't clean up the registry. If so, then uninstall from the "Control Panel", "pray it cleaned out everything FNV related", reboot, and re-install again. (The "reboot" is necessary to release system related files that have been deleted on disk, but not from the system memory.)
So, if you can't even launch the game, then you have a "bad install". The "F:" drive is fine, and you won't need to run as "Administrator".
If you did move Steam out of the default location, then likely any access privilege problem is one of "File and Folder permissions" on the parent "root" folder under which you installed the games. If this is not set correctly to allow at least "System", "Administrators", and "Users" to have "Full Control" then you can't overwrite other files or make changes. You then need to enable the "Properties | Security | Advanced | Change Permissions" setting of the parent folder to enable the box: "Replace all child object permissions with inheritable permissions from this object", so those changes get applied to the existing files and sub-folders.
Did you re-run the "FNV4GB Patcher", and then the "FalloutNVLauncher.exe" at least once?
With that version of Win10 I am told you should not need to set any "compatibility" setting for FNV. "Compatibility" will not be what is preventing the game from launching.
After such extensive restructuring, we need to forget about all previous symptoms, and start over describing your "current" problem as a "new install".