I am not sure what you think the relevance of when I learnt Irish is. With a living language, it is always open to users to replace existing words (or phrases) with new words imported from other languages. Doing so does not of itself invalidate the original term. Zoo is short for, and is often considered to be a synonym of, zoological garden. If "Gairdíní na nAinmhithe" is a correct translation of "Zoological Gardens", then it must also be a valid translation of "Zoo".
The relevance is that other learners may not be aware that you are referring to an era when the use of z in loan words was generally frowned on, and the "popular" translation sú presented a few problems (as it already had 2 other common uses), leading to the more widespread use of Gairdíní na nAinmhithe on signs in the Phoenix Park.
Nowadays, the spelling zú is widely accepted, so there is no need to pretend that Gairdíní na nAinmhithe is anything other than the Irish for "the Zoological Gardens".
Not really. While Dublin Zoo (founded in 1831) is indeed located in the Phoenix Park, a large urban park (over three times the size of Berlin's Tiergarten), the term gairdín na n-ainmhithe was not used to refer to the Phoenix Park, only to the Zoo.
Until 1983, Dublin Zoo was the only public zoo in the Republic of Ireland. I'm not aware that there were ever any others (there are now a number of aquariums and "zoos" at destinations like Tayto Park), so there wasn't really any need to differentiate between big and small collections of wild animals. There is also a Zoo in Belfast, opened in 1934.
If the aim is to use Irish letters to reflect the sound of "zoo", then sú is no more sensible than mó or bó - a broad s doesn't sound like "z", and, as sú already has a number of competing definitions (de Bhaldraithe used sú in the translations of "exhaustion", "infiltration", "juice", "sap", "suck" and "suction", not to mention "raspberry", "strawberry" and "lemon-squash") adding another meaning for no obvious reason other than that it rhymes isn't actually all that sensible.
As it is clearly a loan word, and the whole point is that it is a short word, and it doesn't have any obvious correlation with anything from Irish history, adopting a new word was the sensible thing to do, and zú meets all the necessary criteria - an obvious loan word, short, and sounds like "zoo".
No. Irish and English both differentiate between the simple present (téann tú - "you go") and the continuous present (tá tú ag dul - "you are going"). The have different forms, and very different meanings.
An dtéann do go dtí an zú? - "Do you go to the zoo?" (ever, on Tuesdays, when the sun shines, etc)
An bhfuil tú ag dul go dtí an zú? - "Are you going to the zoo?" (now)