Why is the plural form used?
It's not plural. It's the noun in the dative case (and the possessive pronoun is correspondingly in the dative case as well).
"mele" is the female singular form in the genitive/dative -- and it lools exactly like the female plural in the nominative/accusative case
It is not plural form. It is dative: to my girlfriend=iubitei mele. The plural: iubite=girlfriends.
What are you referring to exactly?