Please go to Wp Admin -> Ads Listing System -> Content fields -> Edit content field that you want to add on Search, Advance search & on Listing Detailed page, Every content fields have such options like the screenshot you can see below.
If you only select search by this field. it will show in the normal custom form, But if you also checked the box of advance search then it will go in the advance search and only open when you will click on the advance search button.
Also in the content field you can have a selective categories. If you select a specific category then this field will show in the search only when you will select that category in the search bar.