WordPress.org

Which width should I enter?

When in doubt: 0.

Whats difference does it make when I enter a width?

If you enter a value of 0, the width and height attribute are removed. While this plays nicely with any CSS rules, it may be desirable to set these values in order to allow browser to lay out the page before the images are loaded. Setting a width and height allows the plugin to scale these values so they fit int the design. It's basically a setting for purists.

Can I exclude images?

Yes, by their CSS class.

Can I disable the plugin on a per-post base?

Yes, by adding [disable_image_scaling] anywhere in the post.

After editing or changing my theme, the images are distorted again

This might be due to the plugin's configuration. If a target width larger than zero, but smaller than the (new) theme's max-width value is set, the images will be scaled to the given width. Then the max-width rule caps the width again, leading again to the distortion. This is normal behavior; Either set the target width to zero in the plugins' settings (this should be fail safe), or to the matching max-width value.