I think it all boils down to what the word (he's) means in English. I have heard it used as a short form of (he is) "he's been running, he's going to town, etc." I have never heard it used in the form given as an acceptable answer for the translation. I know of no English speaker who would say 'he's the rice and sandwich'.
Maybe it is a case of 'droch Béarla'?
Yes. "the rice and sandwich" is referring a definite sandwich - an rís agus an ceapaire.
It would be different if "rice and sandwich" was recognized as a single thing, like "soup and sandwich" being an item on a menu - beidh an t-anraith agus ceapaire agam - "I'll have the (soup and sandwich)".
If "rice and sandwich" could reasonably be considered a "conjoined NP", like "bread and butter", "fish and chips", "ham and cheese", "tomato and lettuce" or "soup and sandwich", then an could take scope over the whole phrase.
I don't think you can reasonably claim that "rice and sandwich" is a conjoined noun phrase.
I think the misunderstanding is that we're using "conjoined" in two different senses — I'm not talking about compound nouns or fixed expressions, but just phrases that have been joined by a co-ordinate conjunction.
So in English, the phrases (1) [DP the [NP [NP rice] [Conj and] [NP sandwich]]] and (2) [DP [DP the [NP rice]] [Conj and] [DP the [NP sandwich]]] can both be grammatically well-formed and they are equivalent in meaning, even though "rice and sandwich" don't have a strong collocational attachment.
And I'm wondering if there's just something different about Irish determiners or conjunctions that forbids constructions like (1). Is it maybe that rice is an uncountable noun and sandwich is countable?
Would "an [ris agus bainne]" or "an [ris agus uisce]" where the definite article still takes scope over both nouns be more grammatically acceptable than "an [ris agus ceapaire]"? Or would you still have to say "[an ris] agus [an bainne]" to ensure both rice and milk are assigned the definite property?
I'm not really familiar with any work done on that sort of sentence analysis in Irish, but the first question you would have to confront is how the lack of an indefinite article in Irish affects your definition of what a DP is., because [DP the [NP sandwich]] and [DP a [NP sandwich]] aren't equivalent.
Normally even in languages where there's no overt articles in certain contexts the phrase structure is still represented, just with a null symbol in determiner position. If I wanted to represent the phrase structure tree of "a sandwich" I'd probably just write it as [DP [D ∅] [NP [N ceapaire]]]
agus is a conjunction that usually means "and", but it can also mean "while" or "as" in certain constructions. It has zero connection with agam and aige (just as "and" has no connection to "an" or "any" in English).
aige and agam are "prepositional pronouns" - combined forms of the preposition ag and a pronoun - mé ("I"/"me") in the case of agam and é ("he"/"it") in the case of aige.
The most common (but definitely NOT the only) place that a beginner will encounter agam and aige is in a phrase with the verb tá, where it is used to show possession - tá úll agam - "I have an apple", tá úll aige - "he has an apple". Compare to tá úll ag Pól - "Paul has an apple" to see that agam and aige are combined forms.
Okay let me word it better, sorry. This structure is not how I (Individually) was taught. "A" is not there when you read the sentence...it is incorrect. It is correct without the a unless the sentence was worded differently. It is again different from how I was taught.