What is the ruling on a man kissing a non-mahram woman, and do the intention and nature of the kiss determine the jurisprudential ruling, and is he obliged to marry her as expiation for his sin?

Kissing and similar sins and transgressions that have no prescribed legal punishment (hadd) or predetermined penalty necessitate seeking forgiveness (istighfar) and increasing good deeds, as good deeds expiate evil deeds. This is in accordance with the Almighty's saying: "And establish prayer at the two ends of the day and at the approach of night. Indeed, good deeds do away with evil deeds. That is a reminder for those who remember" (Hud 11:114). The ruling on such acts does not differ based on intention, but the sin and burden may increase if there is audacious transgression of Allah's sacred limits, and it may lighten if accompanied by humility and brokenness. One is not obligated to marry the woman to expiate the sin; rather, it is obligatory to conceal her sin and your own.