7) While I was researching skate boards, I found an interesting old newspaper story.

8) In the June 29, 1999 edition of the Mercury, there was an article on skateboarding.
9) Some scientists in San Francisco, California filmed skateboarders in action.
10) As they studied the film, they noticed some rules of science at work.
11) To be a good skater, you have to follow safety rules.
12) Yes, skateboarding is not only a sport, but a science.
13) When you balance on a skateboard, there are three forces at work.
14) The weight of the rider is one force, and gravity is another.
15) Pushing up against the skateboard, the ground also acts a force.

Are these correct?

7, 8, and 9 each need another comma.

The rest are correct,

Based on the information provided, it appears that statements 7-15 are correct. Here's an explanation of each statement:

7) While I was researching skateboards, I found an interesting old newspaper story.
Explanation: This statement simply highlights personal research on skateboards and discovering an old newspaper story.

8) In the June 29, 1999 edition of the Mercury, there was an article on skateboarding.
Explanation: This statement specifies the date and publication of the article about skateboarding.

9) Some scientists in San Francisco, California filmed skateboarders in action.
Explanation: This statement mentions that scientists in San Francisco recorded skateboarders performing tricks or maneuvers.

10) As they studied the film, they noticed some rules of science at work.
Explanation: This statement suggests that the scientists observed scientific principles or laws being applied in the skateboarders' movements while analyzing the recorded footage.

11) To be a good skater, you have to follow safety rules.
Explanation: This statement emphasizes the importance of adhering to safety rules to become a skillful skateboarder.

12) Yes, skateboarding is not only a sport, but a science.
Explanation: This statement asserts that skateboarding is not limited to being solely a sport; it incorporates elements of science as well.

13) When you balance on a skateboard, there are three forces at work.
Explanation: This statement mentions the presence of three forces involved when maintaining balance on a skateboard.

14) The weight of the rider is one force, and gravity is another.
Explanation: This statement identifies two of the three forces involved in balancing on a skateboard: the rider's weight and the force of gravity.

15) Pushing up against the skateboard, the ground also acts a force.
Explanation: This statement adds that the ground, when pressed against by the skateboard, exerts a force as well.

Overall, it seems that the statements are correct based on the given information.