The app does not support custom lists, only the Watch List.
You can reach your Wish List on a phone by using a browser; request the desktop site version of the page, go to your Watch List, then use the large "Watchlist" heading drop-down menu to reach any of your custom lists.
Alternatively, you can use a browser in desktop mode to add an item to your Wish List, then at the top of the item page you should see a link to that list in the blue band.
Not sure why your app shows fewer search results unless you have the app set to show you only newly listed items; if so, try searching again to see all results, or disable that setting.
