I have come to the conclusion that the answer to this question is not "settled law" (as we would say in the US, at least). As I read it, the directive and the Schengen codes taken together clearly say that the 90/180 rule does not apply to a non-EU family member traveling with an EU family member, but some seem to think that Directive 2004/38/EC applies only to family members who actually reside in an EU country other than their own. National authorities seem to take different positions on this question; my mother has been allowed to leave France without trouble after spending 4 consecutive months there with my EU-citizen father, even though they reside in a third country, but some questions here have shown that the authorities of other countries do not agree.
My interpretation depends on the fact that the Schengen Borders Code explicitly excludes "persons enjoying the right of free movement under Union law" from the definition of "third-country national" (Art. 2(5)(a) and 2(6)). As far as I can tell, the idea that the directive only applies to those who reside in an EU country other than their own arises from Article 3(1):
This Directive shall apply to all Union citizens who move to or reside in a Member State other than that of which they are a national, and to their family members as defined in point 2 of Article 2 who accompany or join them.
In my opinion, "move to" is an unfortunate choice of words, because it normally means "to establish one's residence in," and I am fairly certain that this is not the intention here, for two reasons. The first is that if the usual meaning of "move to" were intended here, it would not make very much sense to follow it with "or reside in." The second is that the corresponding phrase in the other language versions of the directive do not imply a change of residence. For example, the French is "se rendre," and the German is "sich begeben," both of which would perhaps better be translated into English as "travel to" or even "go to."
Suppose a citizen of an "Annex II" country (allowed to stay 90/180 days in Schengen w/o visa) is married to an EU citizen. The Annex II country citizen can then, for example, stay 90 days in Schengen, leave for 1 day, and then re-enter with their EU citizen spouse and stay for another 90 days (or however long they want, for that matter, provided they apply for a long term residence permit when applicable).
In fact, if my reading is correct, there is no need to leave the Schengen area.
Question 1: What about the reverse? I.e. suppose a citizen of an "Annex II" country stays in the Schengen zone for an extended period with an EU citizen spouse, and then both leave the Schengen zone together. Can the non EU citizen then return the next day and spend 90 days as a tourist?
If the non-EU family member had a residence permit during the extended period, the answer is unequivocally yes, because of Schengen Borders Code Art. 6(2) ("Periods of stay authorised under a residence permit or a long-stay visa shall not be taken into account in the calculation of the duration of stay on the territory of the Member States"). If not, then the non-EU family member would likely be excluded from the Schengen zone for 90 days unless and until the EU family member could join him or her.
I don't think there's any way around this. A similar situation exists with countries that have bilateral agreements allowing three-month visa-free stays. If I recall correctly, the US and Denmark have such an agreement. This means that a US citizen can spend 90 days in, for example, Sweden, and then cross into Denmark for an additional three-month stay during which the traveler is forbidden from going to, for example, Germany. But it doesn't work the other way around, so a US citizen can't use the Denmark-US bilateral agreement to remain in Germany or Sweden immediately after spending 90 days in Denmark.