1.It should be 'You almost missed the bus'. You need the past tense here. 2. 'Let's go to his home' is perfectly correct. A home is where someone lives. So if you go to where that person lives, you are going to his home. Yes, 'home' is a concept rather than a physical object, but that doesn't mean that you can't go there - we use 'home' in contrast to 'work' or 'school', for example. A house is a specific type of construction - a self-contained residential building, usually occupied by one family/set of residents. If the person doesn't live in a building that can be described as 'a house', it isn't strictly correct to say 'go to his house'. He may live in a flat/apartment, (or a caravan, tent or igloo!) . In these cases, 'home' is more accurate than house. I'm not sure what point this book of yours is trying to make, but it isn't being very helpful.

IMHO: Home is a concept, an emotive term. House is a place, a destination, a place you can go to. I doubt that "go to his home" is grammatically incorrect, but not really so common a thing to say. If you have to choose, choose house. Example: "I'm going home" is a common thing to say.