Here's a little copy-paste from the way I learned basic copular rules
Quote:
Here. How about this.
So, I'm going to describe this in the way my class was taught. It'll be watered down, because y'know, we were first semester Irish students without much grammar knowledge. So, your word order is going to be VANTP.
V = verb
A = Indefinite nouns
N = Names
T = Definite nouns
P = Pronouns
So that's your general order. If you use a definite noun, a proper noun, or a name, you need to include the pronoun (*é*, *í*, *iad*, *srl* - note, after *ní*, these prefix an "h") before the first one.
So in your first sentence you have and indefinite noun (*araicnid*) and a definite noun (*an damhán alla*). So, putting these in order (A before T), you get *Is araicnid an damhán alla*. However, you need the pronoun before the definite noun. Since *damhán alla* is feminine, you use *í*. This giving you *Is araicnid í an damhán alla*.
Your second one you have a name (*Pól*) and a definite noun (*uachtarán na hÉireann*). So, putting those together, you get *Is Pól uachtarán na hÉireann*. Yet, you still need that pronoun. *Is é Pól uachtarán na hÉireann*.
Hope that helps explain it a little. And note, this is really basic, and barely scratches the surface of the copula.
1) Since neither of your samples have an N or a T, but only a P and an A, you would fill those in:
V - A - P
An - bean -- t(h)ú?
An - cathaoir -é
ea could be used, but it would be a focus structure in the Caighdeán (yet another reason I really dislike how DL teaches Irish is that it just throws multiple forms with different nuances together...), so I'll leave that out for now.
2) If there isn't a T/A, you'll use 'ea'. So you'll either answer with 'Is ea' ('sea) or 'Ní hea'.
If there is a T/A, you use the correct pronoun:
An é an fear é (Is he the man?) -- Is é ('sé)
An tú an múinteoir? Is mé.
3) In the standard, you're supposed to use the gender of the thing being referred to. Generally, I think most dialects have started defaulting to é tho.