I appreciate your views, as they remind me to bring up a few things to clarify certain points. 

First I'll take the debate with Hagrid over Harry--Severus isn't totally sold on Hagrid's theory yet.  He still has reservations over the kid, but the specter of possible suicide makes hims et them aside . . .for now.  As a former attempted, and a teacher, Severus cannot ignore Hagrid's insistence that Harry is depressed, he knows what went on in the graveyard and knows the pressures of the tournament, and he trusts Hagrid when he says something might not be right with the boy . . .after all the man saw that he was suicidal at that age too and nobody else did.  Hagrid's instincts are good, so Snape accepts the possibility that Harry is very depressed and maybe even suicidal, God help him if he ignored it and the kid died . . .that outcome actually happened when I was in middle school, one of my classmates killed himself, he was 14, and the teacher suspected something but never followed up and to this day has never forgiven herself.  It was a tragedy.    And as a former teacher, I know that teachers HAVE to take even suspected attempts seriously and follow up and mention them to counselers and principals, and I'm sure it's the same in Britain too.  So Sev isn't going to blow off  Hagrid.  But there will be plenty of arguments between the two concenring Harry as the story progresses and Harry remains among the missing.  Like I said, Severus still thinks Harry is a chronic troublemaker and lives to drive him insane. 

Draco's entering the potions lab wasn't too unremarkable, though Severus normally locks the door, but he was in too much of a hurry and forgot.  And he figured no student would be dumb enough to test his wards and actually steal from him personally, especially one of his own House, so yes, he's regretting that too.  Sev's magical wards only extend to his quarters in regards to his signature, not the potions lab, since he holds class there. 

Lastly with regards to Sev and the hawk bonding, I know Severus just throws caution to the wind here and allows his emotions to dictate his actions, and that's a deliberate action here.  Rationally he KNOWS it's not a good idea for him to adopt this injured animal, not while he has to serve Snake-Head, but he cannot help himself.  That's his weakness, everyone has one, even super controlled spies who pride themselves on their logical behavior like Snape.  He knows he should allow Hagrid to take care of the bird, that will be brought up next chapter, and yet he finds he cannot bring himself to do so.  The hawk gives him something he needs--companionship--and his saving its life creates a kind of bond between them that's terribly hard to just shrug off, when you've held a creature in your arms and fought for its life, it changes you forever.  Snape, at least in my opinion, is not as hard as he thinks he is, and though he won't admit it to anyone except Hagrid, he badly needs a friend, though he will be horrified when he finds out just who he befriended later on . . .very much so! Though eventually he will come to accept it. 

Hope this answers your questions. 

Severus will be very shocked and angry at first but after what will happen as the story goes on, he won't be too horrible to harry once he calms down.

I'd agree, they probably do, except I think the teachers aren't allowed to use magic to punish students, which is why they assign detentions without magic.  But losing privlieges is good and yes, they really screwed up big time!