Hello Cheri,
I'm in training to teach
ESL, and questions like yours help me analyze my own language.
You have actually captured, in your examples, the correct usage for 'may' when requesting something in English. We typically use 'may' when 'I' is the subject of the sentence, often asking permission: "May I help you?" "May I use the swing?" When asking someone for help, we use "Will you please...?" "Would you please...?"
Hope that helps!