Diode circuits are quite confusing, if you don't find a "method" to procede solving them. Particularly if you try solving circuits with diodes and opamps...

The simplest way that I have found is to suppose the diode as open, as a first thing, which is usually easy to calculate (in the OFF state current is known, while in the ON you only know it's positive). Then, if the resulting voltage is higher than the threshold, the OFF state is not consistent, and you are sure the diode is ON. In this last case, you substitute the diode with the voltage+resistor.

This is right also for Zener zone, you just have to consider the proper voltage value and direction.

For some circuits with multiple diodes, you should consider all of the cases, preferably starting with the OFF state.

I also found useful to consider current direction when inductances are connected to diodes (as usual in power switching circuits).

Besides all of this, one always have to use good sense, and discard solutions that are not consistent, or intuition to rapidly solve.

A rule that always applies to physical systems is that if the model is right and you find one solution, that is the RIGHT solution. So, if you analyse one of the diode states and find it is consistent, then you have found the solution.

BTW, null current and voltage equal to the threshold is at the limit between OFF and ON state, but a component with null current is simply equivalent to an OPEN circuit.