The Drawn cards markers allow you to keep track of how many times you have played a card that says: Draw one strategy card. In effect, allowing you to replace the card you just played. You can only do this three times in one turn. Of course the colors are not ideal, the idea was to mimic the vassal ones that are blue and red for allies and Japan. but they are distinguishable (white and yellow letters) so just agree which one corresponds to a side.
The stars and roundel used to be "abacus" style markers to help keep track of combat strength when resolving battles. Now you can use them to mark Progress of the War hexes on the map.