Wiring for stairway & two lights on landing

It doesn't matter. The 2-gang switch can be viewed as two separate, unrelated switches. You can simply ignore the switch that is not involved.

Sometimes you get cases where they are entangled, e.g. if supply hot comes to one switch then hops from there to the other. In that case you can get some terminal blocks and change it to a pigtail arrangement that splits to both switches; or change it so it hops to the other switch first (i.e. move the hot wire from the wall). Either method will make the 2-way switch simple like you expect it to be.

I am a huge fan of marking traveler wires using an appropriate color of tape or sleeve (they can be the same color; there's no need to distinguish travelers from each other, but it really helps to know they are travelers). 2-way circuits are quite complex until you get the hang of them, but the biggest confusion is the travelers are the same colors as other wires which are not travelers. It makes things a lot simpler if you mark them.