Out of all you have listed, you can do everything except greatly alter the organization of the theme and provide your own fonts.
You can preview everything at Appearance -> Custom Design in your blog's Dashboard. You would need to buy the upgrade to save changes, but you can preview for free.
http://en.support.wordpress.com/custom-design/
Regarding fonts not loading immediately, this is normal. If the font does not already exist on the visitor's system, it has to be downloaded by the browser before displaying, but it usually takes less than a second. Most people don't even notice it. For example, these forums also use a webfont.