We know, by conservation of energy :

Therefore,

Putting given values, we get :

Therefore, the spring be compressed to 6.93 cm to send the ball twice as high.
Hence, this is the required solution.
Answer: 0.2m
Explanation: Firstly only the Rocket's Weight Compress the spring which can be found by

According to Hooks Law

The part b and c of this question is done in the attachment
Answer:
The box of rocks will have depression which can be seen without touching the box.
Explanation:
The density of rocks is very large as compared with napkins. So, the weight of the rocks will be much more greater than that of napkins.
As both boxes have same volume the heavier box will show depression on the lower surface as compared to the lighter box. So, the box of rocks will have depression which can be seen without touching the box.