I mostly agree with you, except:
beneath 3: unclear what you're saying about this one. "the chair sagged under his weight" is fine (to my ears).
beneath 4: an also use "beneath": "a warm heart under a gruff manner", though I agree that "beneath" would be more common.
under 4: I think that this usage can also sometimes be replaced by "beneath", as in "beneath the legal age". (I'm surprised that Merriam-Webster doesn't offer this meaning. However, there is a difference, and maybe a finer analysis is needed here.)
Also, there are a number of other usages beyond the Merriam-Webster usages. For example, see Encarta beneath (http://encarta.msn.com/encnet/features/dictio...
too low in status or character for, as in "beneath contempt"
Several additional usages, most of which cannot be replaced by "beneath"
[Wow, I wouldn't have thought of all these uses until I saw them in the dictionary.]