The slot option lets you change which of the four save slots the game will save and load from. This includes the in-game save blocks and save menus. Selecting save will save your current game state to the selected slot as though you had used a save block. Selecting load will load the save file saved to the selected slot in a very similar manner to loading a file from file select.
Save files can be saved to and loaded from an SD card with the export and import options if playing on N64 or Wii VC. Pressing either one will bring up the file browser. Importing a file will immediately load a save, but none of the current in-game save slots will be overwritten unless done manually afterward. Exporting will save the file selected by save slot, not the current state of the game. The file extension used for save files on disk is .pmsave, and the default filename is file. The filename can be changed by pressing the name field. Pressing clear will set the name field to be empty. When the name field is empty, the default filename is untitled. When saving, pressing the name of a save file in the file browser will copy that name to the name field. Pressing accept will save the file to the current folder in the file browser with the specified file name. If the file exists, you will be prompted to overwrite it.
Your story progress is the main byte that determines how far you've progressed in the story. See this for a list of what each value corresponds to.
quizmo determines how many of Chuck Quizmo's questions have been answered successfully. This byte also determines which question Quimo will ask you next, and it's used in conjunction with your story progress to determine whether Quizmo can spawn. The three toy box options determine what Kammy Koopa will spawn in Shy Guy's Toybox. Pressing restore enemies sets all overworld enemies to an undefeated state.