How does isometric contraction work?

Question

1. What exactly happens to myosin during isometric contraction? I suspect that either myosin heads just "freeze" in the middle of crossbridge cycle, or go through full crossbridge cycles repeatedly at the perfect rate so that the rate of extension becomes equal the rate of contraction (basically, a muscle isn't still, but repeatedly extends by like <1mm, and then myosin immediately contracts to compensate for this extension to keep muscle at static length - and so back'n'forth it goes).

2. Why isometric contractions spend energy, when physics make it clear that energy is spent only when we change velocity of something? If my second hypothesis is true and the muscle isn't in fact still, then energy is obviously being spent. But if myosin heads freeze in the middle of the cycle glued to actin, there's no reason why energy should be spent.

3. Say, a person is trying to lift a 10-ton rock with all the strength they got. It's also an isometric contraction, but in this case, the second hypothesis shouldn't work, because if myosin could finish a crossbridge cycle under such resistance, it would mean that the muscle is strong enough to lift the rock. So in this case, it must get stuck mid-cycle, with the mass of the rock not letting it to finish its conformation change. If so, then why do muscles spend energy then? Myosin is literally stuck in place, and until it finishes a cycle, it won't bind another ATP.