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: 
Other than any hard-coded URLs, no, your code shouldn't know about the difference, nor care.
The code does not need to be changed, other than to change all links from `http://` to `https://` (seriously, don't forget that, else you aren't using SSL...)