In the hidden object games can we move on after both clues are received or do we need to master each..

If you find the 2 clues and have the required number of Flowers, you can move on to the next scene. However, you'll need all 10 clues and 20 filled stars before you can start the 6th scene, the Adventure Scene, in each chapter. After that you may proceed to the next chapter given that you have the required Flowers. But you will be missing out on 1-star or 5-star boxes, which may contain valuable items. Some players strategically wait to fill the 4th or 5th star until they have Help Wanted cases asking to "Beat your own score".