How are boulders formed on asteroids? For example: Are they soft landed meteorites? Or do they form from melted material during a violent impact? Or are they the result of some kind of erosion process?
It looks like you are asking about rubble piles, asteroids that are made up of a large number of different sized objects that are weakly held together by gravity. A few of the component objects are large, but most are very small (down to grains of sand).

By way of analogy, think of playing pocket pool. Rack the 15 target balls but leave the rack on. The cue ball bounces off when you strike the rack with the cue ball, but that's about it.

Now let's try again, but this time with the rack removed. To make the target balls a even more rubble pile-like, we'll use a piece of cardboard to add a bit of space between the target balls. Now something very different happens when the cue ball strikes the target balls. The balls are only loosely connected to one another. This makes them very good at absorbing the momentum of the cue ball and at distributing the energy and momentum throughout the rack. Given a low to moderate cue ball velocity, the collision will be close to purely inelastic.

And that's how you get a rubble pile. It's one inelastic collision after another after another. Over the course of 4.6 billion years, you have a pile of dust and sand with some rocks and a few large boulders mixed in.