In 'The Speakeasy,' Yumeko discovers a secret at St. Dominic's that has the potential to alter the dynamics of the school's gambling system. However, specific details about the nature of this secret are not provided in the available summaries.

While the episode does not delve deeply into Yumeko's past, her mysterious background is mentioned as a factor in her actions. She continues to disrupt the school's power structure with her gambling skills, driven by a desire for revenge.

The Student Council is not explicitly mentioned in the summaries for this episode. However, Yumeko's actions are generally aimed at challenging the existing power structures at the school, which likely include the Student Council.

Characters like Ryan and Michael appear in scenes with Yumeko, but they are described as feeling one-dimensional and underutilized. Ryan is involved in a heartfelt moment with Yumeko, while Michael discusses stopping her with others.

The episode revolves around a high-stakes environment where gambling determines social status. Yumeko's involvement in these games is crucial as she seeks to make the Top Ten before the end of term, but specific details about the games themselves are not highlighted in the available summaries.