1. How did Roosevelt create the modern presidency?

2. How did Roosevelt's intervention in a coal strike set a precedent for federal arbitration?

TR threatened the coal company owners that if they didn't compromise with the striker that he would send in the military and they would lose control over the company.
3. What did Roosevelt do to the trusts and railroads?

4. What legislation passed during Roosevelt's presidency protected citizens?

The Meat Inspection Act. This protected the american citizens by making their meals safer and the employees of the meat packing companies by making their working conditions safer and more sanitary.
5. What did Roosevelt do to protect the environment?  

Roosevelt was a conservationist. He set aside thousands of acres of land in the west for public monuments or parks. Any money the parks made would go to building infrastructure like dams and water for houses.