How can I specify the style of the z-block (its background color, font, etc.)?

The Z-Blocks extension inherits the style of your theme and usually there's no need for additional adjustment. By using the HTML code in Z-Blocks, you are able change blocks as you like.

If you want to change styles of your z-blocks, you can put it inline. For example:

Before:

After:

Certain CSS skills are surely required.