Can the forms incorporate Google conversion codes and other codes?

Also, can the forms incorporate Google conversion codes and other codes?

May we know what conversion codes you are referring to? We do have Google Analytics widget that you can add to your form. Here's how you can add a widget: https://www.jotform.com/help/252-How-to-Add-a-Widget-to-your-Form 

Note that if you are incorporating a script code, then it is not possible to incorporate it directly in the form builder. You can, however, do that by simply downloading the form's full source code, here's how you can download that code: https://www.jotform.com/help/104-How-to-get-the-Full-Source-Code-of-your-Form. After downloading, you can add your own custom scripts or code, but you'll need to embed it on a web page. 

I hope that helps.