You can put the html for the entrance page (where you enter your name) on your site, but it opens a new link to the conversation page. About the best you can do is theme the conversation page to look like the rest of your site.
You can look at some of the contents by choosing "View Hal's Brain" on your options page. It's more or less necessary to combine training with viewing the brain to see the results, as the words or phrases which actually parse in training need to be checked. Examining your conversation logs and choosing "alter this response" is the usual training method.
The UltraHal Rep has a lot of issues. I hope Robert will get them worked out soon.