Hazy is constantly getting into fights, since his attitude and confrontation nature makes him very prone to fights. Hes tough but always gets hurt in the fights. Here he got ass beat by some bigger foal who was trying to steal his food from him. He doesn’t plan on letting them go.
As I said, Hazy has a foul mouth so he cusses a lot and is generally obscene when it comes to his way of talking. Most ponies in Ponyville don’t know what to do about him and his language.
Being as poor as he was, Hazy has never actually seen a cake before. He’s had candy but never cake. His new mom (though he refuses to call her that) introduced him to her friend Ms Pinkie Pie. After she heard that he’d never had cake before, she started baking him dozens of pies and cakes to make up for his short life of dirty candy that had been dropped on the floor.
Hazy is not used to affection or touches that aren’t violent. He still flinches when ever Twilight hugs or touches him. In all honesty, he doesn’t trust Twilight. He thinks that she sees him as a pity case and is just pretending to care for him. As such, he stole some of her stuff from the castle and tried to sneak off but was caught by the guards. Twilight, for some reason, forgave him and hence this scene.
While it took Hazy a while to trust Twilight, he bonded with Sirius quite quickly, admiring the colt for his detication and honor. That and he was notoriously easy to fool into giving him bits and taking him places. A few seconds of puppy dog eyes and Hazy could get almost anything he wanted. But Sirius was constantly bothered by other ponies at the time and Hazy defended his kind of brother. No one but him was allowed to bother his dumbly naive big kind of brother (or his DNBKB for short).