Can I download the form I created into a fillable PDF document?

I'm not interested in using this as a survey that people submit. Is there a possibility to use this as a document I can download and continue to use as a fillable document without using the website as a retainer?

You can convert your form to a fillable PDF document.  Here is more information on fillable PDF forms:

https://www.jotform.com/help/312-Fillable-PDF-Everything-you-need-to-know-about-JotForm-Fillable-PDF-Creator

There are limitations on what can be translated to PDF form as described in the above guide.