Grammar – How to Use ‘At Home’ vs ‘Home’ Correctly

I'm not an English major, but I am a native speaker.

"I'll bring you home" is definitely not invalid; it's a perfectly fine thing to say, and I think your meaning is correct.

However, "I'll take you home" does not imply that you live at the same place, or that you're going to be staying over. I think it just implies a sort-of dominance on the role of the speaker. I would imagine this being said by a person speaking to someone who is more drunk than they are, or by a speaker who knows the way home better than the other person. Although, to be fair, it probably depends a lot more on who says it, how they say it, and exactly how they phrase it and not so much on bring versus take. For example, "I can take you to your place" has essentially the same meaning as "I'll bring you home."

I think the most natural thing to say in the case that you are both going back to the same place, or both heading home is "Let's go home."

The short answer is that you may employ the simple past perfect to express a continuing action only when the expression is atelic or bears in context a reasonably natural atelic interpretation.

A telic expression is one which has a goal or ending point "built in" to its sense—finish, for instance. Employing the test suggested in the article linked above, it makes perfect sense to say He finished in an hour, but not (normally) He finished for an hour.

Expressions which do not have such a goal are atelic. In your first example, work is an atelic expression: using the same test, He worked for an hour is acceptable, but not (normally) He worked in an hour. Atelic expressions are, so to speak, inherently continuous. Consequently, a simple past perfect construction use supports a continuous sense; this is why the two are "interchangeable".

Your other examples, however, are telic. Eating dinner and cleaning a room are not (normally) protracted indefinitely, they come to an end when the dinner is consumed and the room is clean. Consequently, using simple perfect constructions implies completion, and if you want to convey that the action continues you must employ a progressive construction.

Note, however, that "telicity" is a very subtle matter in practice. As the linked article tells you, grammarians are in some disagreement over just how it works; and I have been careful to qualify all my analyses with the (normally) tag.

Note, too, that there is an alternative to the two constructions you illustrate. The past progressive ("I was eating dinner when ... " and "I was cleaning my space when ... ") is more natural to my ear than the past perfect progressive. You want the past perfect progressive only if you employ a qualifier like since dawn, which removes the focus from the present-in-the-past to the past-in-the-past, the stretch of time which preceded the present-in-the-past.