I agree with LoveChaCha. Looks like his whole cage can be considered a litter box with litter covering the bottom. Did you choose to do it that way due to litter box habits? What are his current litter habits? It looks like there are a lot of poos outside of the box near the hay rack. Bunnies definitely poo while they eat hay and it may be helpful to put the rack near the box or vice versa, so he can sit in the box and eat. If you are able to get him litter box trained, then you could take out the shavings completely.
As far as the hay, is it coming out from the rack? Or is the hay being tracked out by your bunny?
If part of it happens when you actually put hay in the hay box, then what helped me was to get a small laundry bag, fill it with hay, but leave about a foot from the top empty. Then I would take the bag over to the hay rack and pull the opening of the bag over the the hay rack (And that is why having that empty part on top was helpful. Then I would reach in and pull the hay out. In your case, you may have to really make the hay into a ball before you pull it out of the bag to minimize it flying out. Hay is tricky like that!