That rear mudguard is definitely fitted incorrectly and, imho, unsafely. The guard needs to be fixed at the chainstay bridge, even if that leaves it a bit higher at the back - You might need to acquire a
chainstay bridge clip if you haven't already got one. As others have said, safety releases (e.g. SKS Secu Clip) need to be fitted to the front. Once the correct fittings have been sorted, the stays will need trimming to give a good curve around the tyre without the varying gap that they currently have - sometimes a spacer is needed between the rear mudguard and the chainstay bridge. You might need to alter the height of the seatstay bridge clip too - usually there is some vertical movement afforded by a slot rather than a round hole where it bolts on to the bridge.
EDIT: That rear guard does look short.