Adverbs, prepositions, nouns, "home", and "about"

The Cambridge Grammar of the English Language takes home to be a preposition and a noun, but never an adverb. In all your examples, it would be a preposition. Similarly, about is always a preposition. The other two, six feet and my height are both noun phrases.

Part of your problem, I believe, is a confusion between category and function. This kind of confusion is rampant. Even though six feet is always an NP, it can perform various functions including: subject (e.g., six feet is too much), object (e.g., His height has reached six feet), and modifier (e.g., a six foot point guard, ok foot not feet).

In I saw a man my height, the NP my height functions as a modifier of man.

Finally, according to CGEL, yesterday is a pronoun. In those sentences, it is functioning as an adjunct.