Well, key events in the 'ice king marceline story' include the Ice King's various kidnappings of princesses that Marceline has to deal with. There was also an event where Marceline and the Ice King got into a big fight over a magical artifact that they both wanted for different reasons. Additionally, the times when Marceline has tried to help the Ice King regain some of his humanity by sharing her memories of him as Simon are crucial events in their story.
In the 'ice king marceline story', a significant event is the Ice King's repeated attempts to win over princesses, which sometimes annoy Marceline. Also, there are times when Marceline's music has an impact on the Ice King. For example, it might calm him down or make him more introspective. And the time when Marceline discovers some secrets about the Ice King's past through her own investigations in the magical realm of Ooo is quite important.
One key event is when the Ice King's actions accidentally disrupt Marceline's territory. Another is their occasional team - ups, like when they face a common threat in the Land of Ooo. And there's the time when Marceline tries to make the Ice King remember his past as Simon.