The items that appear under each of the "Browse by" fields (e.g. Freelance, Full time, Internship, etc), are set up in the Jobs > Job Types, Job Categories, Salary pages in the JobRoller admin dashboard. These are the default options available in the "Browse by" sidebar widget and it would require customization of the default theme on your part if you were looking to add other search criteria outside of those configurable in the admin. You'd also need customization to actually display subcategories of these as the default is also only for the parent item.
Editing the main search bar would also require customization. Our themes are not encrypted, so you are free to make modifications if you wish. Thanks.