"Month of June" is also accepted, mm? ... Seeing as this is following the forms of 'Mi na Nollag' ie "month of the Christmas' for December, and 'Mi na Samhna' ie "month of the Halloween" for November, is it safe to guess that 'Mí an Mheithimh' might be interpreted as "month of the midsummer"?
Genitive - "the month OF Christmas/December". Feminine genitive nouns use na as the singular definite article. Nollaig is a feminine noun, so mí na nollag. Meitheamh is a masculine noun, so mí an mheithimh.
Do yourself a favour and only complete one or two crowns for each skill before you move on to the next, so that you can complete the tree, and build up a broader picture, rather than drilling all the way through 5 crowns per skill and getting frustrated because you can't figure out what's happening. Once you have completed the tree at one or two crowns per skill, you can go back and add more crowns to your skills.
teanglann.ie has been super helpful for me. If you can't listen for any reason, two of three were vehev. Couldn't really hear the Ulster pronunciation as I'm in a loud-ish environment.