-ing Clauses.
1. Riding on the roller coaster, I broke my hand.
2. Reading news every day, you will be aware of what is hapPening in the world.
3. Having have HAD breakfast, we went to the cinema.
4. The hunter came across with a bear while walking in the forest.
5. When riding in the car, be careful!

'to ride a car' means to be a passenger, otherwise 'to drive a car'

-ing Clauses.

1. Riding on the roller coaster, I broke my hand.
2. Reading the news every day, you will be aware of what is hapening in the world.
3. Having had breakfast, we went to the cinema.
4. The hunter came across with a bear while walking in the forest.
5. When riding in the car, be careful!

No. 5 is ok, although I think it would be better to change the phrase order: "Be careful when riding in the car."