Welcome to you and Eugene! Kira knows more about kittens than I do. Her advice is good. I adopted two Persian littermates from a rescue shelter when they were over a year old. They are doll face Persians, so I don't think it is necessary to pick their noses.

They do snort and snore a bit, though. My two don't always cover their business either. When I adopted Humphrey, I was told he never makes a practice of covering up, but he does it now and then. I never taught him, but he is a pretty clean kitty. The other one, Bogart, does his best to cover up, but ... well, that's a long story ...
Your Eugene will get sufficient nourishment from the wet catfood. It also insures he will get enough water for his system. Are you feeding him the same food he was eating with his breeder? Or is he a rescue? The change of food and the stress of the move could be affecting his poops. If it does not clear up, then a trip to the vet's may be in order.
To post a picture, open an account on Photobucket or some such website and store your photos there. When you click on a photo in Photobucket, a menu will drop down and you can copy the IMG code and paste it in your message. I hope that kind of makes sense.