They seem to automatically potty train themselves. This breed is amazing. Even at 7 weeks, ours never messed in the house, he immediately ran to the door and looked at us with a desperate, let me out I have to pee kind of look. They are very calm and gentle but understand, if you don't instruct early and often as to who is in charge - you, holding the end of the lead, when they are over 100 lbs and full of locomotive steam speed, you won't have control. Leashes are not a form of punishment for guardian breeds at this age, it helps them understand boundaries.
He's just doing his puppy play thing with your beagle and she's too tired for puppy energy. I love beagles - any hound dog is a good one.
As Mulemom mentioned above --"Anatolian shepherds are far more trainable in general than Great Pyrenees. You have to remember these dogs have been bred for centuries to be independent thinkers."
She is correct and they don't really care about obedience training; i.e., sit, stay, here, down, etc. They just want to do their job. For me, it's about their temperament. There are vicious ones with high kill drives, rare but they do exist - we had one. It sounds like you have a good guy though so that's awesome. Enjoy puppiness.