My apartment has something called a tankless water heater. I think a lot of apartments here in Taiwan have that. Mine uses gas from a steel tank. When the tank runs out of gas, I call up a company that provides these tanks (their phone number is usually painted on the tank), and they send someone over to replace it with a full one. It’s not expensive.
Here’s a thread in which there’s some discussion of this kind of water heater: How do hot water heaters work here
I don’t rightly know what to tell you about winter clothes, because while a peacoat sounds like a good coat for winter in Taiwan (or the other coats you mentioned, for that matter), and while you might be more comfortable in a coat you already own, housecat’s right that you’ll most likely be able to get what you want here (or at least what you need) in the way of a coat.