"mac" is of the first declension
confirmed by the dictionary, which also shows its masculine...
rules for first declension are here
so far, "mac" nom. sing. has modified to "mic" gen. sing. Now final rule: possessive pronoun "mo" causes lenition / eclipsis.
Go raibh maith agat, A shcilling!
Yes, I can see here how the indefinite article + noun can be considered partitive, so it fits this scheme.
Also it seems from this reference as if the partitive dative is also a possible subtitute for the the partitive genitive, when the first noun is definite?.....
my quarter of the apple = mo cheathrú an úill = mo cheathrú den úll ?
However the dative can only replace the genitive in the partitive aspect?
the taste of the apple = blas an úill != blas den úll
where "!=" means "is not equal to"