Kirchhoff's loop/current rule is just law of conservation of energy and Kirchhoff's junction rule is just law of conservation of charge.So, I think that these can be applied to any circuits unlike Ohm's law. Is there any exceptions?
Kirchhoff's loop rule is also called Kirchhoff's voltage law (KVL). Which is different from Kirchhoff's current rule which is also called Kirchhoff's current law (KCL). KVL is derived from Maxwell–Faraday equation for static magnetic field (i.e. the derivative of B with respect to time is zero). KCL is derived from charge continuity equation which is equation 3 here.
A well known case in which KVL doesn't apply is when having a varying magnetic field enclosed by the circuit being studied. The presence of time varying magnetic field makes the measured voltage non-unique (depends on the branch used to measure the voltage). Have a look at page 3 of this presentation.
A well known case in which KCL is limited is when having a voltage source with very high frequency such that effects like parasitic capacitance can no longer be ignored. In those cases wires (or conducors) are treated as transmission lines. In such a case a current can flow even in an open circuit..
For further information have a look at limitations sections of KCL and KVL here.
Yes, until energy is conserved.
Kirchhoff's law is amongst great basic laws which help in constructing electronic physics.
Kirchhoff's law is based on the Law of Conservation and we also know that energy is always conserved according to our latest experiments and analysis. If in future it gets false then we must once have to think about the applicability of Kirchhoff's law in that particular condition.
But, till then Kirchhoff's law can be applied on any circuit with a loop or junction.
Also, charge is conserved similarly.
Ohm's law has drawbacks, you can read them at Draw Backs of Ohm's Law
No, there are no exceptions to Kirchhoff's Law till now.
Also pls refer @WetSavannaAnimalakaRodVance 's comment in below comment line.