Most definitely a stalker. He'll even use his invisibility cloak to stalk you from time to time, so if you ever wondered what the gentle breeze was around you even when you weren't near any windows and didn't see any ghosts? Well, that's Harry for you. But he won't be doing it so frequently since well... with all the people in the wizarding world trying to capture him and kill him and all that

You'd either be in his class or you'd be on one of the Quidditch Teams, doesn't matter which house or he probably met you through mutual friends between you both like Hermione or Ron or Ginny or even Neville for that matter. Or maybe you might've been there for him when Ron was ignoring him during the Triwizard Tournament and telling him to do his best in a friendly way and not behaving like an over obsessive fan girl like Romilda Vane

Eventually, the 2 of you would meet (Or me might even use the Marauder's map to see what you're up to and then 'coincidentally' bump into you) and become friends and who'd pass the opportunity to become friends with THE Harry Potter?

Will fall for you even MORE if you're not like an obsessive fan or something and you believe him when no one else does. Like the Putting of names in the Goblet of fire in the 4th year and the Dementor attack on him during the summer. He admires you and loves for sticking up for him especially against Malfoy. But he kinda feels ashamed of himself since you're gonna be dealing with Malfoy's wrath as well and that's why he'll do his best to make you avoid Malfoy as much as possible

Best if you don't leave anything of yours behind since he's gonna use the summoning charm to get little souvenirs for himself be it some candy wrapper or ring or whatever it might be. He'll want it and love it if it's belonged to you

He will tell you EVERYTHING that went on in his life to you and besides, that's the first step towards a relationship right? No secrets... oh wait... you guys aren't dating yet. Oops... but he doesn't mind it at all, you'll be dating him soon enough anyways. He'll even tell you about all the adventures Ron, he and Hermione had and his friends might think it's weird and strange. The secretive Harry potter spilling his guts to someone he barely even knows? Yep, definitely not strange. He won't even bother denying that he knows Parseltongue

He is one HELLA PARANOID person and you can't exactly blame him here since he's already lost most of his loved ones. So, if he doesn't see you for a while he'll be getting anxious and he'll snap at any and everyone till he gets the news that you're safe and everything's fine with you. What if you were kidnapped? What if some scumbag Death Eater captured you in your sleep? What if Voldemort was trying to kill you? You could be in severe danger! So, this boi here tends to cause scenes after he sees you be it in the Great Hall during breakfast or at class or even the damn Quidditch Pitch. And if Malfoy sees it, even BETTER since he knows Malfoy has a tiny crush on you and although more better to rub it in his face while he looks at him with a smug AF expression on his face

He'll be a blushing nervous mess if you come to his Quidditch matches but he'll be determined to win and catch the Snitch as fast as possible since he really wants to impress you. And maybe do some really cool tricks with his broom along the way if he can

You'll catch Harry following you in his invisibility cloak one day and after you catch him, you'll confront him about it and he'll tell you that you need protection and he's just making sure you're safe and he loves you and needs you. So, you'll start running but it's gonna be in vain since he'll capture and detain you somewhere. Not in the school since it might be risky but somewhere in the Forbidden Forest most probably

He'll send the most nasties and scariest glares ever to people who ask him about your disappearance and tell them to drop it. His friends won't have solid and concrete proof that he did something to you and they don't want to accuse him of something they aren't sure of. So, he'll be off the hook

Back to him keeping you locked up in some god forsaken place. If you're being adamant and refusing to love him you better pray he isn't considering wiping your memory and casting a Oblivion charm on you to make you forget things because that's EXACTLY what he's thinking about right now. He might ask Hermione about it and as usual, she'll give him the perfect and most detailed answer and if that doesn't work.... well, the Unforgivable curses are always there

No doubt by now he must have become one heck of a twisted whackadoodle and he needs to protect you and it's for your own good and if he has to hurt you to make you think you'll be safe with him then so be it. He might use the Cruciatus Curse on you for like 10 seconds and every time you scream he feels like crying and holding you and begging for your forgiveness but he HAS to make sure you behave well for him. He'll to the begging and crying part later. And of course, the killing curse is always there for people who get in his way and try taking you away from him