Question: My server provides SSL connections via https, although the certificate costs extra...

Is there anything that needs to be changed in the PHP code to utilize this protocol?

My site has:

* ajax forms via POST
* regular forms and pages using POST and GET parameters
* Session variables

Answer: 
You should be good to go. PHP does not impact the use of SSL or not.

Things you should check are:

* Are all URLS in you application relative (no `http://`)
* Are assets (CSS/JS/IMG) used in your site (***both from internal*** and external sources) also as relative paths or prefixed with `https://`

Having an asset without `https://` in a SSL powered site, the browsers will warn you visitors that something ain't right.
Other than any hard-coded URLs, no, your code shouldn't know about the difference, nor care.