What are the different conflicts in The Great Gatsby besides the main conflict of Jay Gatsby trying to win daisy back and relive the past as if nothing has changed?
The central conflict, as you have identified, concerns Gatsby's aims to win Daisy. Within this conflict and existing alongside it are other, smaller conflicts.
Daisy's troubled marriage to Tom and a possible meeting between Daisy and Myrtle can be seen as another conflict in the novel. Certainly, the tensions within the Buchanan household should be seen as a conflict.
Daisy's internal conflict regarding which man to choose is a significant conflict as well. She faces a rather serious moment of crisis when Tom and Gatsby have their confrontation. Here we see that the decisive choice that will determine the outcome of the novel's central conflict rests with Daisy. She must choose to stay with Tom or leave him to go with Gatsby. Neither Tom nor Gatsby has the power to dictate this outcome.
Nick's faith in Gatsby is another conflict in the novel. Nick has to decide whether or not and how much to believe in Gatsby - in terms of his story and in terms of his moral value.
Each of these conflicts is resolved during the novel's extended climax (from the confrontation in New York to Gatsby's death).