Would russians use this sentence to mean 'my brother is about to leave'? As an example is english if you're at dinner or someones house and you say "I am going home now" or "My brother is going home now" it means you are about to leave rather than you are currently in the process of "going home". Or would you only use this in russian to mean you are currently in the process of "going" or "walking" home?
There is a slight difference between "My brother is on his way home" and "My brother is now on his way home". The latter is more specific and emphasizes a certain aspect of the situation. Anyways, it's a vocabulary word, and should be noted regardless of how logical the sentence is.
"coming to the house" = "идёт/заходит в дом", not "идёт домой". "Домóй" and "дóма" are used only when you mean home, not any random house.
Go home = идти домой
Go to somebody's house = идти в чей-либо дом
I'm at home = я дома
I'm at Misha's house = я у Миши дома / я в доме Миши. (in this case we can use "дóма" because the building is home for Misha).