Val

This could be caused by having the main landing gear to far in front or behind Center of Mass (CoM).
To get a stable landing gear setup, you want
A main gear lifting the craft as close to CoM as possible without tipping. A nose gear or a tail wheel as far from the main gear as possible. A car type layout of the landing gear, where all the landing gears are located near the ends of the craft can create the symptoms you describe.
Here's a couple examples that are very stable.

I think, you still have to take care with the sequence of attaching intakes and engines, to get the full synchronous flameout.
At least, I still do. When a multi engine craft is done. I rip off all engines and intakes and mount them. One intake and engine pair at a time in symmetry, for each nacelle.

No, not completely.
As far as I know, occlusion by stack connected parts is dependant on the areas of the connecting surfaces. If the next part in the stack has a larger surface than the part in front of it, then it is not fully occluded.
(It's possible that my view is too simplified and there's more too it, but the above should be a usable as rule of thumb)

As far as I'm aware, this is a bug with the Aerodynamics overlay, not with actual lift generated.

Solar power is very weak on Laythe compared to Kerbin. And panels are draggy. I'd go for FuelCells or RTG.
A "car"-type landing gear, with the rear landing gear far back, is generally very unstable on aircraft. Put the Landing gear beneath CoM and Rover wheels further back.
3 engines is a lot for such a small craft. Here's a single engine super sonic craft inspired by yours.
It's stable as an aircraft both on the runway and in the terrain and as a rover on rover wheels. Quite forgiving and robust as you can see in these videos.
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