Proper noun constructions deserve their own little monograph, for both their syntax and their semantics. Here are some remarks on the types you’ve asked about:
(1) Firstname Lastname - Yes, the current analysis treats this as a compound noun with the second element being the head. If there are three names, there is the expected ambiguity, where the bracketing can be either [[Mary Jane] Smith] or [Mary [[Smith Jones]]. The decision to make the second element the head is probably wrong, given the behavior in coordinated names such as “John and Mary Smith” where the resulting NP is plural, not singular, which would follow if the first element were the head. Note also that we should probably block “John Smith and Jones” meaning the coordination of “John Smith and John Jones”, which would be a little easier to do if the compound were left-headed. Perhaps we can have a discussion on the merits of such a change at the summit this summer, before I implement it, since it would have a marked effect on the external interface to the grammar.
(2) Cityname, Statename (and Cityname, Countryname) - Yes, I agree that here too the first element should be the head, not the second one, again motivated by coordination/agreement examples, where “Paris and Lyons, France” is good and should be plural, while “Berlin, Ohio and Germany” should be blocked with the meaning “Berlin, Ohio and Berlin, Germany”.
(3) German Language - The capitalization of “Language’“ here is dubious in my view, since we still have to say “we speak the German language” not “we speak German Language”, treating “language” as a count noun, different from “language” used as a mass noun as in “We should use legal language here”. The word “German” in this expression signifies, I think, the name of the language and hence is a proper noun, so “German language” is a compound noun with the second element a common noun, where we can paraphrase “We speak the German language” with “We speak German”. This is probably different from the use of “German” as an adjective as in “We visited a German city”; note that we contrast “They speak a Germanic language” with the less felicitous “They speak a German language”. This adjective vs. noun contrast is clearer where the name of the country or culture and the name of the language differ, as in “The English language is spoken here”, not “The American language is spoken here” (and of course normally not “American is spoken here”). Further, in “the Australian English dialect” the structure should have the adjective “Australian” modifying the proper noun “English” with “Australian English” forming an NP-N compound for “Australian English dialect”. It would be awkward if English here were an adjective, since [[Adj Adj] N] would force the first adjective to modify the second, or else both adjectives would separately have to modify the noun, not the intended interpretation.
(4) Seattle Airport - These so-called post-title constructions are a little more vexing, since the capitalization of the second element seems to matter, and capitalization is not so consistent. I’m not sure “Seattle Airport” is the clearest example of this type, since it sounds odd to say “We arrived at Seattle Airport” instead of “We arrived at the Seattle airport” (or maybe “We arrived at the Seattle Airport”). So let’s use “Seatac Airport” instead. If the usage is “We arrived at Seatac Airport” (with capitalized “Airport”) I think we still want to treat it as a common noun serving as a post modifier of the head “Seatac”, not as a compound noun (which would be odd in having a singular count noun heading an NP missing its determiner). So this is treated with a special construction in the ERG, making the first daughter the head. (Maybe if we switched to treating “Mary Smith” with “Mary” as the head, we could find a single left-headed construction analysis for both.) In contrast, if the sentence is “We arrived at the Seatac airport” with an overt determiner, the ERG treats “Seatac airport” as an ordinary NP-N compound with “airport” as the head, consistent with the fact that we don’t usually get an overt determiner with compound names: “*We met the Mary Smith today”. Note that the ERG offers another analysis of “Seatac Airport” just like “Mary Smith” where “Airport” is a proper noun that has nothing in common semantically with the common noun “airport”, but when annotating the ERG treebanks, we deprecate these semantically opaque analyses.
(5) “The National Hockey League” - These are the most vexing types of constructions, where there is a multi-token expression for a named entity where it is tempting to try to analyze it compositionally rather than as a semantically opaque sequence of proper nouns. When the named entity has an overt determiner as in your example, we normally choose the analysis where the final word is a common noun and the head of the compound noun phrase (even though “League” is capitalized) to account for the overt determiner. Note that we normally see lowercase for “the” if it’s not sentence-initial: “We complained to the National Hockey League”, not “… to The National…”. But it seems like a road toward madness to try to consistently analyze the other elements of multi-word named entities as ordinary adjectives and nouns to produce a transparently compositional compound structure, since people inventing names don’t always combine the elements in conventional ways.
To summarize a little for these last two types, if there is no overt determiner in the named expression and the last element can be treated as a common noun (capitalized or not), then we treat that last element as a modifier of the compound proper name preceding it (so “George Washiington University” will have “university” as a modifier of the name-name compound “George Washington”). If there is an overt determiner, then the last element is still treated is a common noun, but now it is the head of a compound NP-N phrase so we can account for the presence of that determiner, as in “The National Hockey League”. Finally, for an expression such as “The New York Stock Exchange” we have settled on ignoring the capitalization of “Stock” and “Exchange”, treating “stock exchange” as a multi-word common noun which heads the full NP, with “New York” as a multi-word proper noun that forms an NP-N compound with “stock exchange”. As you can see, this is not the only obvious analysis possible, but offers a pretty good balance among consistent annotation, robustness, syntactic normality, and semantic transparency, even though it achieves none of those perfectly.
and there are a LOT of proper nouns.