"In two minutes" means in approximately two minutes, possibly more, possibly less, but not that much more or less. "After two minutes" means in at least two minutes, possibly a bit more.
You've rightly called out the differences between the first two statements:
He is in a meeting
The above statement refers to the person attending a meeting in the same premises (i.e. on site).
On the other hand:
He is at a meeting
Refers to the person attending a meeting at another premises (i.e. off-site).
Coming to your third statement:
He is on a meeting
The above statement incorrect, and should not be use. The preposition "on" would only be used for calls, such as:
He is on the phone
Although one often hears people mentioning "His is on a call", it is probably preferable to state it as "in a call" to reflect the fact that he is in a phone call. "On a call" tends to give an impression of a professional making a house call (e.g. a doctor visiting a patient, or a plumber at a home for repairs).
Note: the above paragraph was edited based on @user3169's input. The original version said "on a call" was incorrect, while in reality it isn't that black-and-white.
Upvoting your question for the research you've put into it.
Best Answer
I would use in front of the house to describe the position of an object/ a person that is not part of the house and at the front of the house to describe the position of an object/ a person that is part of the house.
→ The car is parked in the garden or in the street, not at the back of the garden and not in front of the neighbour's house.
→ The sundial is on the wall of the house facing the street.
→ The kitchen is at the front, not at the back, of the house.
Where it gets more complicated is when we have sentences like:
Both can be heard and are correct. My feeling - and it is only a feeling for which I have no grammatical explanation - is that in such cases "house" reflects a different thing in the mind of the speaker.
→ I understand "house" as meaning a whole property, more a place than the actual building, I include the garden as part of the house.
→ I understand "house" as meaning the actual building, bricks and mortar so to speak.
Let's have another example:
→ "at the front of the car" here means next to the driver's sit (and not at the back of the car/ behind the driver)
→ I'm talking to someone who is standing right outside the car, maybe leaning on it, or very close to it, but not inside the car.
Be aware that "in front of" and "in the front of" have different meanings:
to me would mean the same as: