Can I just copy and paste my html code that is required into the page?
While you "COULD"... I wouldn't. The first time you, or another user, accidentally switches the view on that page... BAM... it's probably going to mangle your form.
It's much safer to go with a plugin that allows you to use php in your content areas. You'll define all the php for your form in the admin panel.. then enter a "snippet" into your content editor.. which will fire that php code at that point in your content.
This is much better than putting the code directly into the html section of the editor.
Here is a link to a php snippet plugin:
http://wordpress.org/extend/plugins/php-snippets/