Not sure what is happening there. If you are going to use projectors just use the sample as a sample and set up projectors according to latest docs. Could be that new shaders are needed and the ones I include are no good for latest Unity version. Get whatever is latest from the Unity examples/ standard assets,
tldr; choose "check valid" for "extra precision" in height tool options before you press execute.
The easiest way to deal with that problem in shot 1 is to create a smaller grid which fits inside the terrain boundary. You may also move the MapNav object (change its world location) so its nodes overlap nicely. It does not have to be at 0x0x0.
The other option would be to modify the code which determines if a hexa is invalid. That would be in the Height Tool which makes calls to MapNavHexa.AdjustToColliders() (around line 366) in MapNavHexa.cs
You will see a ray is cast down the centre of the node and it just happens that the edge of the terrain is on these centres and therefore the node is included.
One would need to calculate the position of the 6 corners of the node and cast rays down those, as an addition if centre cast succeeded, to makes sure all 6 are valid.
But, looking at my code again, it seems I did include an option for this (see line ~390). You just need to select one of the "extra precision" options in the Height Tool options; for example "check valid".