Can't speak of other languages, but in German anyway the sentence is exactly the same. "Ich bin zuhause" meaning word-for-word "I am home". Same issue, normally a location would have a preposition and an article. Reasoning is also the same as in english, "home" and "zuhause" are not a location but a state in this case.
Yes, "home" and "zuhause" mean the same thing but they aren't exactly the same, zuhause is a compound word. English also has compound words, for example "aboard" and "abed". The English word isn't "ahouse"; it is simply "home".
True. I was more going on the idea of OP that it must confuse english learners. I often feel people who only know one language tend to forget that most latin languages tend to have similar quirks, often making such quirks in a foreign language rather natural.
In this case, it's nothing to do with Latin. German is not a Latin language, and old (pre-Norman) English is closer to German than anything else. It's the shared Germanic heritage which gives us this quirk.
Absolutely. The fundamental thing about the rules of grammar is that they're more like guidelines. In fact, I think OP's example is hardly the most confusing or inconsistent thing in English, which is not to say that the question isn't a really good one. The quirks, similarities and differences are one thing that makes language-learning really interesting.