Because, although it refers to a female person, "cailín" is grammatically masculine, so the adjective is not lenited here.
When the -ín is a diminutive ending, it makes a word like cailín masculine. When the -ín isn’t a diminutive ending, the word could be feminine, e.g. braillín.
Because that would mean "He is a musical girl".
Grammatical and natural gender don't always agree. In this case you use the pronoun that accurately describes the physical subject, not the grammar.