1) An infinitely stiff kart would only lift a wheel with some lock applied. You yourself agree further down. When you steer the kart, the load on the outside front is decreasing, the load on the inside front increasing. Any flex now will only resist flex whilst the chassis is not stiff enough to support the load at the OR, IR, and IF. Once this point is reached, unless load is transfered to the OF, the OF lifts. You can see this for yourself when steering the kart on the dummy grid.
Once load transfers to the OF, and you have cornering force, the increased load on the new points of contact, OF, OR and IF, flex the chassis even more, steering can return to straight ahead, but the IR does not fully load up again until we're accelerating out the corner in a straight line.
2) Yes, you can lower the CoG, but again, there's only so far you can go, usually limited by the bottom of the seat. Sure, you can tip the seat back, but there's only so far you can go. You can change ride heights also, but there's only so far you can go. In some classes you can run out of adjustment range to use the extra grip effectively. When you start two wheeling a kart and you're already as low and as wide as you can go, what do you do?
A cadet kart that has gripped up is very slow and the engine runs significantly hotter. They're already as wide and low as they can go. What do the do?
Further, I never said you can't move the centre of gravity, I simply said it can only be lowered so far, and we're all usually pretty close to as low as you can get. Our centre of gravity is very high for a racing vehicle (more correctly, our track width is very narrow for such high grip). You'll never see an F3 car two wheel through a corner.
3) A rotating axle in flex is very similar to a mass, spring, damper system. Pick a point on the axle (when view from the side). When the axle is in flex, that point is in compression at 0 deg, nothing at 90 deg, tension at 180 deg and nothing at 270 deg. Plot that on a graph and you'll have something that looks remarkably similar to that of the mass, spring, damper system. Since we know the "spring" aspect is largely constant, and the "mass" aspect is the load placed on the axle, the only bit left to change is the "damper" aspect. An increase in damping will reduce the amplitude (flex) of the wave.
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