I've noticed that there are several Irish dialects and that Duolingo often says "In some dialects it's like this and in others like that", could you please tell me if the dialects can be understood by every native (and non native) Irish speaker, and which dialect is the Irish lesson on Duolingo teaching us?
Go raibh maith agaibh agus slán :)
Here is a map of Ireland:
There are three main dialects of Irish
Munster (closest to the standard language)
Connaught (one of the most popular, I think it's the most spoken too but I'm not sure)
Ulster (mainly spoken in Donegal, it's the most different dialect)
There are also various smaller dialects spoken across the country. For example, the Irish I speak is from Southern Leinster.
The dialects are mutually intelligible - a lot of the difference can be put down to accent, and the same difference occurs in English (I once shared a house with a guy from Donegal. For the first month or so, I couldn't understand a word that he said).
Until the 1970s, when Raidió na Gaeltachta was set up, native speakers from the different regions didn't have much opportunity to hear one another, unless they met in Dublin or London or Boston or New York or Chicago. Since then, familiarity with the other dialects has increased, so that the different vocabulary and grammatical differences are not a major barrier.
Though it is worth noting that there are "fluent" non-native speakers who can't understand natives, like the lady mentioned here who can't understand the people on TG4 or Raidió na Gaeltachta.
But, generally, there really isn't a big difference and they are all mutually intelligible. Native speakers, as you said, get along easily enough with the other dialects after a little exposure (even the synthetic forms in Munster and cha in Donegal). Learners might struggle a bit at first if they haven't learned some of the non-standard things, but it'll come fairly easily after exposure.
The course is based on "An Caighdeán Oifigiúil" (http://www.oireachtas.ie/parliament/about/rannoganaistriuchain/ancaighdeanoifigiuil/). This is a written standard for grammar only, and doesn't specify pronunciation. (Strictly speaking, it doesn't include spelling either, but spelling in Irish has a "de facto" standard, as reflected in the major Irish-English and English-Irish dictionaries at www.teanglann.ie and www.focloir.ie)
The speaker used on the course appears to be from North Connacht, and occasionally uses dialect forms of words that do not reflect the text exactly as written. (Equally, she sometimes follows the text as written, even though her native dialect might not normally use that form).