Picture two appears to show a brake caliper with a ferrule that doesn't fit into it. That's why it is sticking up and cockeyed.

There is no rule. Component makers can choose to use ferrules or not. Shimano chooses no ferrules at the lever or caliper. Sram uses them at both. Old bikes generally didn't use brake ferrules, but clearly those levers are made for them.

It is easy enough to see what fits and act accordingly.