I was thinking of right transfer orbit combined with exactly right aerobraking, though I'm not sure if Mars has a dense enough atmosphere even if you were aiming for a flyby 1 millimeter above the surface (and that's assuming an indestructible Roadster)...
You need a third body to pull that off, and I think Mars’s moons are too small to be useful for this.
Looking at practical considerations rather than just theoretical, you also need the ability to perform course corrections along the way. The initial trajectory won’t be precise enough to make it work from just the departure burn.
Yep. Real-Scale Solar System provides that. There are also mods to add real-world rockets (like the Falcon Heavy) and real-world aerodynamics (Ferram Aerospace Research).
To do a gravity assist you do not need anything more than Newtonian two-body interaction. KSP already has that.
You can think of it as a small ball (the vehicle) bouncing of a big heavy ball (the planet), but the forces are not those of elastic compression, rather those of gravity.
Really itching to install some Kerbal Space Program mods and try to figure it out...