Is there a way (setting or plugin) to make the size selector wider? So that I have more precision when changing the brush size. Currently it's too narrow and I have lots of free space to the right.

What kind of precision are you looking for?

I usually type values directly into the slider or use the scroll wheel. I also have multiple copies of brushes saved with common brush sizes, so I can easily switch back and forth. Have you tried the "quick settings docker"? I personally don't like it but some might love it.

-Keith