Have you gone into the Options screens? Under System Options there's an interface that lets you move around a lot of the UI elements. Also, on the game screen itself if you click the touchpad "button" it frees up the cursor, which you can move around with the touchpad and highlight, grab and drag certain things like the message windows/logs. You can also use it to command pets by using the cursor to select actions on the pet hotbar that comes up when you have one summoned.
If you read through the "getting started" blurb for PS4 off the main page of the Lodestone it will explain how to control the cursor with the touchpad. For example, if you highlight a tab and double-tap, but hold on the second tab, you can grab the tab and adjust the size and position of the UI element (I did this to resize the game logs in the lower left-hand corner).