I actually don't use the Kobo app to read on my tablet because I mostly read sideloaded books from my Calibre Library and the Kobo app only syncs Kobo books.
I use Aldiko(http://www.aldiko.com/
) which has different "sorts" for its' shelves such as "Recently Added", Recent Reads, Author, Title, Recently Finished,Books by Rating.
I generally add the books to my tablet in the same order as I add to Calibre so that my Recently Added list is in the same order as Calibre sorted by Date Added. I delete the book from the app (tablet) once I've finished it so it is no longer on my shelf in Aldiko (but it is still in Calibre). You can add a custom column in Calibre to track read vs unread, you could use the instructions in the Shelves sticky on the Kobo reader forum for the Calibre instructions.
As for covers, you may want to use the Modify ePub plugin to run any books you added to Calibre in so that the metadata is corrected in the file. I'm not sure why but the old cover (or old missing cover) stays in the file and that is why you are not seeing the cover. If your book is run through the plugin (correctly configured), the new cover will replace the missing or legacy cover. There is a thread in the Calibre forum about using the Modify ePub plugin.
Concerning shelves in the Kobo app itself, perhaps someone else can help you...I've only used shelves on my Mini. I would think it would work in a similar way, you can create a "shelves" column in Calibre and have the Kobo pick it up from there on the e-readers. Not sure about the Vox, I gave it away before trying this out on it.
The shelves sticky is just below the Vox forum in the Kobo section.