Displaying data is completely a client-side issue. If you want to display the result "on the current page", you will have to make the submission and retrieval through JavaScript, likely through some library that abstracts away the nasty machinations of Ajax.

If you "don't have a lot of time too read up on it in full", I can only suggest you trade time for money and hire a consultant to implement a solution for you.

Also, I can only recommend using CGI instead of hand-rolling your own request parser. Also, sending mail without verifying that the input fields look like you expect them to is often fraught with problems.