The "Prev" button only appears when the game is able to rollback to a previous picture. The randomiser and preloading features make the "previous" button a bit unsafe, this is really just a "oh I didn't wanna skip that last one" button, one time undo.
It isn't visible, but there is a lot of under the hood stuff to make pictures load before they are shown. Otherwise new pictures would constantly be loading as they are displayed (and it is still the case if you press "next" a bit too fast, depends on your internet speed and size of picture). If you play the game without skipping pictures, there is normally enough time so loads are done before displaying pictures.
The Itch browser doesn't seem to allow opening a new tab or window, only navigating to a webpage but then you would be out of the game and stuck on e621. I really don't think anything can be done about that.
If it's both really important for you to play in the Itch.io app, and to see the source, I can try to display the URL when used in Itch, so you can at least copy the URL and open in browser.