German here. These are some cultural and day-to-day differences compared to the US:

• Sundays are officially a day of rest and so most shops and businesses are closed that day, with several exceptions like high priority stuff, restaurants, tourism/event-related stuff and so on. But you can’t go to a regular supermarket or expect a package delivery on a Sunday. Although some sundays are also different, it’s like an “event” where regular shops open sometimes. But that’s rare.
• Cash is still very widely used (and you also should generally use it even if it’s less convenient because it’s probably the most privacy-preserving payment option), but other payment options are also available almost everywhere
• There are tiny fees of around 1 € you probably need to pay when e.g. going to a public toilet or using a shopping cart. You also need to pay extra for bags, or bring your own.
• Tip culture is very different, Germans usually pay very small tips compared to the US and no one expects you to, but in restaurants it’s common to tip something like 2 € for a bill of 25 € for example. Or you simply round up the number to avoid the hassle of small coins.
• Prices always include taxes already
• Water isn’t free and usually you can’t order tap water, although tap water is drinkable generally
• You can drink alcohol with fully visible labels/bottles in public
• For bottles and cans, there’s a “Pfand” which is like an extra deposit. So a bottle of water usually costs slightly more, but when it’s empty you can return it to get the extra deposit value back. It’s to encourage recycling.
• Germans are more reserved in public and might do less small talk, and are usually more direct, but that doesn’t mean they’re unfriendly. This also applies to customer service! Personally I like this more than obviously fake and exaggerated politeness.
• You should be more quiet in or near residential areas between like 10pm and 7am
• Punctuality is highly valued, this is actually not exaggerated or a myth. Public transport might not wait for you if you’re 1-2min late. People will assume that something’s wrong when you’re a couple of minutes late to an appointment.
• Highways have no speed limits in parts but you still probably shouldn’t drive much faster than 130 km/h. Pass other cars only on the left lanes, never on the right lanes. Also don’t drive on bike lanes.
• Basically all streets or public spaces are safe to walk around. Also children don’t need supervision.
• Most Germans have very good English skills, except maybe very old generations