@Paradox
They exist insofar as they are derived from models applied in the right contexts. But I'm not sure if it would be reasonable to speculate they exist beyond that. The questions I asked would become relevant then: if regularities arise from objects with arbitrary properties relating to each other rather than from a universal constraint on those objects, we should not really talk about "laws" (except for ease).
The "law" metaphor itself doesn't even work too well for current physics since current physics describes and predicts based on mathematical expressions and equations first and foremost. Rules, conditional or otherwise, for how a thing must act or react (what the efficient causal chain should be) take an almost secondary role. We know x will happen because e=mc^2, rather than because x must be an effect of P which needs to be its cause. There's actually an interesting book that talks exactly about this, claiming that physics actually doesn't care about efficient causality. And afaict, "laws of nature" are essentially universal rules about efficient causation. QM blows a hole into causation of this kind as well by challenging local realism.