1. how do I publish my forms to my website?

You can publish you form to you website by getting the code from the embed wizard, I recommend using the iframe method as it will prevent conflicts with similar scripts on your site.

http://www.jotform.com/help/67-Which-Form-Embed-Code-Should-I-Use

This guide will show you how to achieve this http://www.jotform.com/help/34-Adding-a-Form-to-a-Web-Page