Etiquette Hell

Getting cashier's to address customers by name probably increases the chance they'll recognize people and so address them in a friendly, personal manner eventually... but what about customer's who don't want to be recognized? I think the woman who comes in on the Saturday with her husband and buys lots of diet meals, but then comes in on the Monday to buy several liters of chocolate icecream, would prefer a cashier whose half zoned out and doesn't remember their last few purchases
However, ma'am and sir aren't very common around here. I've always taken Mr/Ms LastName as the more distant, polite manner of address - its being addressed by the first name that would seem too close. I'd be bewildered that they'd worked out my name and probably dislike it, but at least they were calling me Ms Lastname rather than Geekette.

I'll admit, this practice sets my red secure-all-personal-info flag on fire, but I'm also a lot twitchier about that sort of thing than most.

Seems to me that this is exactly the purpose of LinkedIn

exactly.

your note is fine. when you reach out like that, it makes you look proactive which is [usually] a positive trait in an employee.

good luck!

Seems to me that this is exactly the purpose of LinkedIn

These are my reactions to what you wrote:

He said "Are you mad at me? Because you're usually very nice and last time I came over you seemed annoyed with me." He was very spazzy when he said it...

Yellow flag. Maybe he's being honest and trying to communicate. Maybe he's being manipulative and pushy and trying to get you to overcompensate by being super nice to prove that you're still a nice person.

he told me "Your lights were on and I knocked,  but you didn't answer."

Yellow to red flag. Stalker behavior. Pushy to tell you that to try to get you to JADE (justify, argue, defend, explain) to him. Not his business why your lights were on. He could have made the observation in his mind and made a mental note, but he's not your keeper, he has no business "calling you out" for allegedly being home and not answering your door.

To this, I might have replied "Oh, that was the night I was super constipated and was on the toilet for 2 hours. Oh, my poor hemorrhoids" just to not reward his pushy comment and shut him up.

He also told me yesterday that I look tired.

Yellow to red flag. He's either rude and mean and trying to put you down because he's a jerk and he likes to push nice people around. Or he's just socially awkward and clueless. Either way, so far, he's not seeming like the kind of person I'd want to spend tons and tons of time with. I'd cut him loose as an acquaintance. No need to answer the door anymore to anyone who hasn't told you in advance that they're coming over. For a while at least, till he learns to stop.

I know I could take him on if he tried to attack me unarmed...

And if he were armed?

There's no reason to be opening the door for him. You care about his feelings. More than you care about your own? Ignoring his knocks/rings isn't mean. You're not telling him to go jump off a cliff or have a miserable life. You're just living your own life. If you want to spend your evening on your couch picking lint out of your belly button and have no other reason not to open the door, you still don't need to. You're not responsible for his feelings, or to make sure that he has friends or is socialized or instructed in considerate behavior.

he asked me how I profiled him when we first met...

Another yellow flag. Awkward behavior, IMHO.

I'm a crime buff, I'm a little extra paranoid (which makes me less trusting in general).

My opinion is that you're not paranoid. I've lived in big cities and heard lots of stories. I think everyone should have a peephole or a side window and shouldn't open doors unless they know and fully trust the person on their doorstep. Again, JMHO.

How old is the brother?  It might be worth having a "man-to-man" with him (well, woman-to-child, but you get the idea) explaining that part of growing up is taking more responsibility for yourself and that includes bathing regularly.  Even if he's not old enough to be setting his own bedtime schedule and *really* bathing himself, a one-on-one talk might help break down any resistance that he has, and it would give him the chance to bring up any issues (such as the water being turned off or the sister being so tired in the evenings that she can't enforce it) even if the sister hasn't been comfortable sharing about them.