Battery requires contact. This is why involving a whole second, and much larger, body of rules is probably a bad idea. If you think RAW is confusing or obtuse, boy, wait til you check out the common law.
This isn't true. RAW gives us a test. I don't know why you have discarded it.
The context is "any rule that refers to an attack."
Yup. Also, this adds in the concept of attacks that do not target a creature or object, so you have to deal with that.