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1) When addressing two people by name, do you repeat the vocative particle for each? For example, would you say "A Mháire is a Sheáin, tugaigí dom bhur gcótaí"? My inclination is to say yes.
It is yes... because why wouldn't you put the second name in the vocative? You call the 2nd person too...

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2) If you're using the form "is as Éirinn dom" to say where you're from, the emphatic form would be "is as Éirinn domsa" rather than "Is as Éirinn mise," yes?
Yes. But "Is as Éirinn mise" is just as right, it's the emphatic version of "Is as Éirinn mé", which is the same thing as "Is as Éirinn dom(h)".