Show more questions depending on the user's answer

If I create a drop box, and they choose an option (i.e. yes) can it prompt a new fillable box option and is there anyway to make make my form fit a single page for printing?

You can show/hide a field based on the user's answer. Here's a guide: https://www.jotform.com/help/316-How-to-Show-or-Hide-Fields-Base-on-User-s-Answer

You can adjust the spacing between questions, it'd create a compact layout and would help fit the form into a single page if possible. If not, browsers will automatically create a new page when you print them.

http://www.jotform.com/help/62-How-can-I-change-spacing-between-questions

If you know CSS, you can also inject custom CSS codes into your form to further customize the spacing of the form questions and other elements.