Do the multiplicity of exceptions to grammatical rules in Irish vary by dialect? If so (as they surely must), does the Caighdeán have a list of official...exceptions? If it doesn’t...what the hell do I do? I guess look at Use of the Genitive at Nualeargais to start. Are those rules the same everywhere, and if not...what should learners like me do?

There are differences.
If you're interested in dialects as they are spoken nowadays, it's quite simple: people usually use the genitive case only in certain set phrases. Looks like it's true in all Gaeltacht dialects.

In Donegal, it looks like the lenition and eclipsis rules are kept in the genitive case after the articles, so people say "hata an fhear" (instead of "hata an fhir"), "gúna an bhean" (instead of "gúna na mná"), etc.
And also: "hataí na bhfir" and "gúnaí na mná" in the plural. Ie. nouns have 2 forms: 1 for the singular and 1 for the plural, no matter what case.

What you can do is choosing a dialect and sticking to it. Speak it as native speakers speak it ie. without much genitives, and when you write, use the genitive case when the standard says it's required. Because I think it would look weird if you drop most genitives in writing as people drop them in speech. The people who'll read what you have written will think you don't master grammar But in speech I think it's fine.
Of course you can also use the standard rules of declensions also in speech, but it's harder

_________________
Is fearr Gaeilg na Gaeltaċta ná Gaeilg ar biṫ eile
Agus is í Gaeilg Ġaoṫ Doḃair is binne

Well yeah, sticking to one dialect would obviously work, but it would be pretty weird for me to speak a specific dialect when I've never actually been to Ireland, let alone the Gaeltacht. Much to my surprise, however, the full Caighdeán grammar is available online...for free! I guess you'll be seeing less of me around here (not that I was ever here that much to begin with), but you guys should definitely keep that in mind when you're having trouble in answering questions.

As for the genitive...really? People really say deireadh seachtain, déanamh rud éigin, a lán éisc, and things like that?

not weird at all, other people did that before, including me. I did my best to speak Donegal Irish even before I went there, with all the material I had.



not "deireadh seachtain" because it's a set phrase so everybody says "deireadh seachtaine". But indeed people would say "ag déanamh rud éigin" (in this case anyway you wouldn't have the genitive because an indefinite noun which is qualified by another word, be it adjective or noun, after a verbal noun, isn't in the genitive : ag déanamh obair mhaith). And they'd say "a lán éisc" too.

_________________
Is fearr Gaeilg na Gaeltaċta ná Gaeilg ar biṫ eile
Agus is í Gaeilg Ġaoṫ Doḃair is binne

Why would it be weird? People pick dialects for a variety of reasons. I was interested in Ulster Irish long before I visited there for the first time because so many of the musicians I loved were Ulster speakers. A lot of people lean toward Connemara because it's the most widely spoken. I know people who took up Munster Irish because they liked the sound of it, or because their family came from Munster.

Redwolf

It seems strange to try to pick up a specific dialect without ever having been there when you could just learn the Caighdeán instead. I realize that the situation with English is quite different, to say the least, but it would almost be like trying as a language learner to learn Cockney without ever having been to London.

And alright, let's say déanamh an rud, would it be that or ruda?

Except that no one actually speaks An Caighdeán. It's an artificial construct.

Redwolf

Exactly Redwolf.

No native speaks Caighdeánach. Anybody who speaks it will always be picked out as a learner.

Whereas Standard English is spoken naturally in parts of England. And Standard French is Parisienne.

Another thing to keep in mind...unless things have changed radically, the standard doesn't address pronunciation. It also allows for dialect expressions. So in reality, learning standardized Irish simply means learning a mixture of dialects.

Redwolf