Forms, CGI, PHP, domain hosting and head meeting brick wall!

[#1]

I'm setting up a website for my daughter who has been with Force9 for a long time on dial-up and, on my advice, took up broadband and home phone with them on a Plusnet Value account. The good news is, she has Force9 webspace available from her dialup days but beyond that I seem to be hitting my head against a brick wall at everything else. Advice would be welcome on the following...
My PAYG legacy account allows domain hosting for free and I had presumed the Value account would too. It turns out, after trying to move her domain in for hosting only, that it doesn't at any price. Is there a way round this to get rid of the side effects of framed forwarding (no favicon, the address bar doesn't reflect the current page etc)  from 1and1 where her domain is registered?
I want to include a form on one of her pages but, unlike my account she has MySQL and Front Page Extensions and not CGI. Is there a way to use a PHP or CGI form script in her webspace? If not, can anyone point me to a script that would work in her webspace (it needs to be simple, I'm a newby at this aspect of site construction!)?
TIA

[#2]

Does this feedback form "how to" help?
http://personal-computer-tutor.com/feedbackform.htm

[#3]

Thanks. It was interesting, but I know nothing about FrontPage and I don't have it.
I have managed to put together a form that uses a .htm page which calls a .php file. Is it possible to run this in a Value account's webspace with MySQL and frontPage Extensions present, or would I have to place it in my cgi webspace and call it from my daughter's webspace? As you may notice, PHP is very new to me!

[#4]

For a PHP file to run on Plusnet webspace, it needs to be in the cgi webspace.
If an account has got MySQL and FrontPage extensions, I'm surprised it hasn't also got its own cgi webspace.
Remember that cgi webspace, and MySQL, and FrontPage extensions, and "non-cgi" webspace, each need you the account holder to use the Plusnet Member Centre to activate them before you can use them.

[#5]

Though Plusnet offered Frontpages at one time, this was on a separate server from both normal webspace (homepages) and ccgi space. Due to becoming non-maintainable (Microsoft stopped Linux support in 2006) a security vulnerability led to Plusnet turning off the Frontpages server about 15 months ago.

[#6]

Thanks for all the responses. I've managed to get a resolution to the problems.