Well, web designing is not included in TCH hosting services. But, nothing to worry about, as you can use FREE CMS like Wordpress, Joomla and many more to develop your websites. They are very easy to understand and user friendly. Tutorials are easily available in text and videos on internet too. So, let's start right now. Cheers!
Yes, you can host any domain with TCH whether it is purchased from any other provider. You have to simply put TCH nameservers in your domain control panel and all done. Nameserver propagation depends in your ISP, it may take 1-2 days. You have to wait till it take place. That's it.