So cead means first, but it also means a hundred?
Yes, scroll down in link, also for samples of use, e.g. aon ...
Cead = 1st is not mentioned in the notes.
What is the 'd' in front of Eanáir?
Because the preposition de is being used.
But should de be used here? Wouldn’t just the genitive of Eanáir (conveniently also Eanáir) be needed? Or is de + nominative an acceptable option?
In FGB's example (under 'first') they use de. (An chéad lá d'Aibreán)
Entry number 18 here shows that either nominative use with de or genitive use without de is possible.
Why would you use the preposition "de/d'" here instead of the genitive of Éanair? Come to think of it, under what circumstances in general do you use the genitive over "de/d'"?
In this case, you are referring to part of the month, and this is the partitive de indicating part of the whole.