Yep he's a bit old to still be mouthing. I'm sure someone will have something to add to help with that. I would redirect with an 'anh' and if he continues crate him briefly. For jumping, I would try giving him something TO do. Have him sit. I would ignore him when I come in if that's when he's the most excited and only give him attention when he's calm. Be sure he's had plenty of exercise. Just being outside doesn't mean he actually drains energy.
As to the scratching - it COULD be the difference in temperature from outside to inside and the drier air .. maybe. That's all I can think of at the moment.
It's also possible that he's scratching outside but you're not catching it since you probably don't see him constantly. He probably sleeps most of the time he's outside and waits for you to get home so he can scratch for you.