Earthquakes can trigger aftershocks on faults near the epicenter (or the same fault that generated the quake), and it has been recently suggested that they can also trigger smaller quakes on different faults that are farther away. This is because the energy produced during a large earthquake can shift rock around, changing the orientation of the stress field or frictional properties on a fault. This shift may cause the rocks to move to a more unstable orientation, thus causing slip along that fault.

This was documented in Asia in 2012, when a moment-magnitude 8.6 earthquake in the Indian ocean triggered two 5.5 magnitude earthquakes off the coast of Japan in the following days (Delorey et al., 2015, Science). The authors of this study actually suggest that surface waves are the main trigger for what they call "cascading earthquakes" that can occur after large quake. Basically, as the surface waves move through the crust, they cause several small "cascading" tremors that shift the rock around enough to eventually cause a large earthquake along a large fault. In this case, the 5.5 magnitude quakes happened along normal faults at a subduction zone. However, surface waves (called either Love waves or Rayleigh waves), are formed. Thanks!

S and P waves are what we call "Seismic" waves. This means they travel through the earth, and through different materials. The way they move through materials doesn't inherently causes disturbances. However, S and P waves can cause other waves. When a P or S wave hits a surface, they can create other waves which are destructive. A fault is a type of surface, so it could be effected.

When waves collide with each other, it doesn't have the same result as when solid objects collide. When two waves collide we call this interference because depending on how they collide, there can be different results. The result of the collision can be either destructive interference (one wave cancels out the other wave) or constructive interference (they add together to be stronger).