"Were" in this example is the English subjunctive, which increasingly, outside of formal contexts, is not used. For many verbs, the subjunctive forms are mostly the same as the indicative forms, but with "to be" it is more noticeable because it is obviously different, as you have picked up. There seems to be a pattern of using it in song lyrics, which maybe the writer of the song you mentioned has followed: "If I were a carpenter, and you were a lady ..." "If I were a rich man ..." In my opinion, "If I was a boy" is perfectly correct and normal in informal contexts. I have a vague feeling that in Australia (my country) and in the UK the subjunctive is used less now than in the US.

"If I were a boy, ... I would understand" is a type 2 conditional. More information about "I was" and "I were" for type 2 conditionals: https://www.ef.com/ca/english-resources/english-grammar/type-2-conditional/ [excerpt] It is correct, and very common, to say "if I were" instead of "if I was"