He's just letting you know he has to get up early, so he'd appreciate if you're quiet and don't disturb him later in the day.

If you're not playing loud music/TV, moving heavy furniture late, not having loud company over, and not literally stomping around the house all night, you're probably doing more than he expects. It's not at at all uncommon for people moving in to do that, especially a lot of younger people who will have friends help them move in their furniture in exchange for some drinks and food, which can sometimes turn into a small party.

Relationships with landlords can vary on a large spectrum of basically never seeing them, to being friendly with them. I'd assume because you are renting in the same house or complex as him, you'll likely see him often, but just be friendly when you do. Introduce yourself when you run into him coming or or going, or when he's obviously not busy, and keep things relatively brief by talking about work and any basic questions about the living situation. Most landlords don't do much more than that and whatever repairs and upkeep they're expected to from your contract and state or local laws, anything else is them choosing to go above and beyond, and it's not a healthy business relationship to be close enough that you're being an actual friend and doing personal favors often.

If they're generally interested in helping you learn the area or whatever else, wait for them to offer more than advice on directions, recommendations for finding things locally, and basic questions. Once you make some actual new friends and acquaintances through work, social areas (local bars, hobby communities, church if that's your thing, etcetera), they'll likely be far more willing to help you out. You may even be able to find other immigrants around to help you navigate the transition, depending on where you are.

For example, I'm in New Jersey a bit outside New York City. We have immigrants from just about everywhere, and they often help each other a lot even when they're from totally different cultures and speak very little English. Larger cities or nearby suburbs probably have a lot more people like that, and the locals are far more accustomed and willing to help people like yourself.

Americans have a very different understanding of being polite. Making small talk and asking people about their day, complimenting them casually, and very little thought about age difference or hierarchy outside of more formal work environments. Even then, bosses at places like big law firms and corporations may insist on you calling them by their first name and talk to you about more personal things. If you're ever lost about what you should do, just be honest and say the cultural differences are confusing, and they'll probably help explain it to you.

My best advice is to use reddit and other platforms to ask questions to people local and possibly make friends. Or feel free to message me. I used to be a bit of an otaku as a teenager, am still a huge fan of Mobile Suit Gundam, and that led me to taking an interest in getting a better understanding on actually Japanese culture, though I'm no expert. But if I can help at all, I'm happy to.

First little tip is to try and be brief with messages and don't be too formal or apologetic. Even as an American I struggle with this sometimes, it's just my nature to be polite and thorough)."Thank you. I'll be there at 11pm. I'll be as quiet as possible. I look forward to meeting you in person when you get the chance." You'll better be able to discuss your situation or concerns with him in person.