While I'm not able to pin down your focus in the question, I guess you're having trouble understanding the function of は, in grammar and in mental model. You may have already heard about that は marks topic, which is not on the same level with subject, verb (predicate), or object. What does it actually mean?
Think of a theater, where actors play as they like on the stage. Interactions between actors can be described as sentences using grammatical relations like subject and object. When you say English sentences require a subject, it means that you can't make a sentence until you mention at least one actor. By the way, actors can't perform in the middle of nothing. They can't fight in the void like gods before the world creation. There have to be an implicit scene, a backdrop, a stage. A Japanese sentence requires a topic, that means, you must set up a scenery before you talk about who did what. What becomes topic is marked by は.
Of course, は is not always detached from actors. You can take out one of them and put the one as a background, like a king on the throne in the middle of the stage but does nothing, just signifying they're in the palace now. That makes an element is a topic and a participant at the same time. Such things are marked by appropriate particle + は: には, では, とは, からは etc. Note that が (≈ subject) and を (≈ object) are eaten by は, so when you see a bare は, you must suspect three possibilities: が + は, を + は, and the isolate は.
literally: Tokyo now rain is falling.
No, it's like "Tokyo: now rain is falling."
This is a grammatical sentence but not the most natural one. に used in this manner is archaic or poetic, not in the regular language. は put in the middle of sentence could have various special connotations, such as saying "not snowing but raining" or "raining it is".
The default interpretation of this sentence is, I guess, "It is indeed raining in Tokyo".
If I'd like to tell the meaning in the English-compatible way, I'd say: