With voltages defined as integrals of total electric field, the modern KVL indeed does not hold, because their sum equals minus net electromotive force for the circuit and this emf is arbitrary, depending on how we arrange the integration paths (or wires).

Does Kirchhoff's rule hold?

In circuits on paper, Kirchhoff's law is always true; if the real circuit behaves differently - it means the model on paper is inaccurate, and it can be fixed in this case by adding a transformer for example.

Do Kirchhoff's rules always apply?

Kirchhoff's rules can be applied to any circuit, regardless of its composition and structure. Because combining elements is often easy in parallel and series, it is not always convenient to apply Kirchhoff's rules. To solve for current in a circuit, the loop and junction rules can be applied.