Finally, simulation is coming to Geometry Nodes! I've seen some projects using it and I'm amazed on what can you do with it.

I tried different approach with rotation. I built a tracer with sim nodes, that traces wheels positions and creates a curve path. And surprisingly those newly created curves have tangent, and all we have is to align object to this tangent rotation

This is a great start, and very informative. Unfortunately I don't know enough GN to solve the problem myself yet, but the big challenge with caster wheels is flipping. This solution sets the orientation based on where the current point is now and where it was on the previous frame. The problem with that is if the wheel stops, then change directions, you get a sudden flip. The orientation should work by "dragging" a point along. One way to do this (but setting it up is annoying) is to create a single mostly rigid hair the length of the wheel's radius with no dynamics and put an object at the end of the hair. The caster can then orient toward the object at the end of the hair. It works great, but is a pain to rig. The appeal to GN is setting a node setup so I can put the pieces of a caster in a collection, create a plane like you do in part 2, and then I just need to define the body of the caster, the wheel, and it could take care of wheel rotation based on distance moved in local space, etc. I'm not quite sure how this would work with GN. Really I would do it the same method as the hair for the most part. Draw a line from the pivot point to the wheel center (but keep Z the same and this position isn't linked, it's just for initial orientation). The second point position should attempt to be the same as the previous frame as close as possible while keeping the same length. So as the wheel moves, obviously the pivot point moves, but the other point will move only to keep the line length the same. If it's already out to the side then the wheel will straighten along the animation path. If it's pointing Exactly straight forward then it won't flip around at all, but that's really hard to maintain. With subtle movements the wheels will flip back around.

Thanks, that was full of interesting usable details :)

Is fantastik, (Is there a way to accelerate straight ahead and brake when cornering?)

This isn't what I was hoping simulation nodes would be, this is more like writing your own solvers. I was hoping simulation nodes would be more along the lines of giving objects various physical properties via attributes, and the a simulation engine takes care of the rest (like the current simulation system, but with greater control due to it being node and attribute based). So for example you could set a selection of vertices to act as cloth, and then increase the weight attribute of those vertices in response to collision with rain particles (to simulate cloth becoming heavier and more resistant to bending in a wind forcefield). Another would be reducing the stiffness attribute of vertices in response to collisions with particles that have a high heat attribute set. good for making an iron rod bend as the physics engine considers the changing stiffness and weight attributes of the affected vertices. Or another example, being able to specify the inner_density attribute an airtight object to emulate heavy metal, or a helium filled balloon etc.