Yes to all of your points. To add some detail:

1: Values calculated in VS and send to PS are all (in case a struct is returned) interpolated from value of vertex1 to vertex2 (and3) ?

Not just when a struct is returned. Always when passing data through TEXCOORDs (also called interpolants) they will be interpolated.
As a side note, there is a way to pass the value from vertex1 to vertex2 and 3 without being interpolated, but it's hardly ever used as it is a bit difficult to manage.

3: For a 'smooth' surface the vertex normal should be calculated as an average of the neighboring surface normal.

Yes, though as unbird said, you need to renormalize after the average because it's not guaranteed to be unit-length anymore.

4: For lighting I can either
a - calculate the color at the vertex, based on the vertex normal and lighting formula, and then the color will be interpolated from V1 to V2 (Lamberts shading)

Yes, this technique is ancient and called gouraud shading (very used in the 90's and beginning of 2000) and tends to look very bad by today's standards unless there's a high vertex count. It's very fast though, and sometimes as a nice alternative for mobile games, or in combination with per-pixel lighting (what you listed as 4b) when the light count is very high (i.e. lit vertices with lights 8 to 16 using vertex shaders, lit pixels with lights 0 to 7 using pixel shaders).

These two options are called "forward rendering" techniques (because you lit while you draw).

Though, other alternatives quite different to your options 4a & 4b are deferred shading (called like that because you lit after you've drawn) and forward+ (also called clustered forward, forward deferred; it's more like the forward pass you're learning, but involves a preprocessing step similar to deferred shading); but since you're just getting into shaders & lighting, forward rendering techniques are the best starting point.

Btw. deferred shading & forward+ are just techniques whose only advantage is that they increase the number of lights that can be used in the scene at the same time without hurting performance, normally they don't produce higher quality results than forward rendering (though it's arguable that if you can use more lights with the same framerate, you can make it look better; but it's not that they're inherently higher quality)