Translation:The people of Ireland are very friendly.
Since "daoine na hÉireann" uses the genitive case, the "na" indicates the definite article.
Better/more explanation here: http://nualeargais.ie/gnag/subst2.htm#genitivverwend (in the subsection "particulars of definite genitive-attributives")
No I just can't spell it at all yet or figure out which one to use. I would have never thought to put "na" before it anyway. Sometimes I get very overwhelmed with Duo. I really feel that they have made the course entirely too hard. When I use my books, they are not this difficult. I feel like there are so many words in each section that I am not really learning them. I can recognize them when I see them but I can't remember or spell any of them myself. I keep going on the Irish course just out of stubbornness I guess.
Stick with it, you will get there eventually. It is a big elephant so you can only eat it one bite at a time. Tá sé eilifint mór mar is féidir leat é a ithe ach mhiotóg go miotóg.
When Duolingo throws me a bunch of new words, it can take a certain number of repetitions before they stick in my memory. I simply don't continue with the next section until I feel that I can confidently recall them . I learned that repetition of the same thing over three days is absolutely key and since the "practice" option doesn't guarantee that, I simply go back and repeat the subsections only.
I'm in no hurry to get through to the end because I know that it won't be the final goal. It is just a tool to help get further along. My other tool is a free program called Seans Eile that works as a "flash card" system and helps drill things like the prepositions, comparative adjectives and much more. Barely have scratched the surface of that one so I am not sure that it will teach me some of the idioms that I never saw in text books such as using "in ann" to express "capable of". Duolingo has been doing that for me.