"It is a sandwich, is it not?"
Translation:Ceapaire atá ann, nach ea?
The fact that it's atá tells you that there is an implied (or elided) copula in the first clause ("is ceapaire é atá ann"), and therefore the tag is nach ea, not nach bhfuil.
You wouldn't use it for ceapaire, but you could say of a person and an office/occupation Tá sé ina Thaoiseach, nach bhfuil?.
A sandwich (which) is there vs. It is a sandwich. Ann, generally means 'there. But it varies somewhat. There is little difference in the two sentences you wrote - that is, no significant difference when translated to English, but in Irish it offers the speaker to begin with 'ceapaire'.
Also, I don't think it has the exact same meaning of 'there' in English. In Irish, you would say 'Spring is there' to express 'it is Spring'.
there, that is, 'in existence'.
Aisteoir atá ionam is an emphatic form of Is aisteoir mé used in Donegal and Connacht. In Donegal this construction has even begun to replace the normal classification copula. You would use this structure when you wanted to emphasize that you're an actor, as opposed to a teacher or some other thing. This structure is not in common use in Munster however.
As for why this particular exercise seems to require Ceapaire atá ann... to the exclusion of any other construction I can't say. Both Is ceapaire é, nach ea? and Ceapaire is ea é, nach ea? would do just as well.
ae is the Irish for "liver".
ea is a 3rd person singular neuter pronoun (é is a 3rd person singular masculine pronoun, and í is a 3rd person singular feminine pronoun). ea is only ever used with the copula (is ea, an ea?, ní hea, nach ea, más ea, ba ea, gurb ea, gurbh ea etc). It's not easy to summarize when it is used but it is usually used with an indefinite predicate.