Does what happened between me and the girl count as zina (fornication/adultery) necessitating repentance and 60 days of fasting, given that no penetration occurred?

What you did, kissing, invalidated your fast due to seminal emission, and you must make up that day. The severe expiation is not required. This act is considered a minor form of zina (fornication/adultery); for the Prophet, peace and blessings be upon him, said: "Every son of Adam has his share of zina… and the mouth commits zina, and its zina is kissing." You must offer sincere repentance by feeling remorse and resolving not to return to such an act. Do not despair of Allah's mercy, for Allah forgives all sins. And in the future, beware of being alone with a non-mahram woman.