You are being presented with a golden opportunity to learn to alter your style of interacting. You can grow through this, so that you establish a more appropriate distance between this guy and yourself and, also, raise your level of competency in how you'll handle interactions, going forward, with whomever you meet.

You tend to feel other people's pain. You take s lot of responsibility for trying to prevent whomever you're with from experiencing pain or, even, mild discomfort emotionally. You tske too much responsibility. To stop doing that you're going to have to be willing to stp rescuing others from the consequences of their own social ineptness and disregard for proper boundaries. At first, doing this is going to make you feel ruthless and unkind. You'll have to tolerate that, as you build this skill. Stick with it, and you'll learn how to convey as much warmth as you wish, while, at the same time, blocking others from intruding into your space and your time beyond where they're welcome.

Your apt is your domain. You are the queen of that space. Make it a policy that you do not welcome visitors showing up without calling first. So, if someone just shows up at your door, always say, "I'm afraid I'm in the midst of something, and I can't have a visitor right now." Letting a guy like your neighbor in is problematic because it may be hard to control how long he stays. Better to chat with him outside, so you can conclude the chat and withdraw from him when you like.

After just a few weeks, you don't really know how nice of a guy your neighbor is. He may seem inoffensive in his manner, but that doesn't mean he's nice. You believe in giving people "the benefit of the doubt." Unless, and until, a person acts badly around you, you go on the presumption that they're probably decent. That's dangerous. There are loads of twisted, creepy people out there. Until someone demonstates their goodwill and integrity over an extensive interval of time, you don't know what they're made of. Be pleasant and courteous to most everyone, but allow for the possibility that anyone you know little about may have a past darker than you could imagine. Him looking you up and down is weird. I've never known any normal guy who does that. This neighbor of yours sounds lonely. He may be alone because people who get to know him a bit don't stick around long.

Whatever you do, don't accept an invitation to catch a movie with him or to do anything of a date-like nature. If you do, he'll glom on and be a worse nuisance. 8:30 pm is late to be knocking on someone's door to give them mail. The mail thing sounds contrived to me. Do not open your door at that hour to anyone you were not expecting. He could have left s note on your door about that.

He's testing your boundaries. Firm them up. When he pushes past where he should make up any old excuse to deflect him. Don't worry if he believes you or not. Giving him a flimsy excuse can be an effective way of letting him know that you need him back away from your space. Good luck.