Do I need to use the DocSearch UI or can I build my own?

DocSearch crawls your site and provides an initial UI, but you don't need to use it. 
If you want to use the DocSearch UI, you can follow the instructions here.

If you decide not to use the DocSearch UI,  you can use the index name, the application id, and the search key to populate your own autocomplete instance which is a UI library provided by Algolia.