In a federal system a citizens role is to choose who represents and makes decisions at the state level and national level. In a confederation the citizens uphold the most power. They choose representatives for their states who posses all the power. Lastly in a unitary government the people hold the least influence. All the power it held by the national government. This leads to the citizens and subnational governments depending on the national government.
I understand the system of division of power as government authority being decentralized. It is balanced between multiple powers so that one power does not overthrow or overpower the other.
The federal government shapes states with its federal grants and loans that it distributes. It forces states to abide by certain criteria in order to receive these grants and loans. They also shape states by recommending guidelines during certain events. For example the CDC a federal agency recommended wearing mask and social distancing during Covid 19. This caused the state of New York and other governments to issue mask mandates and social distancing guidelines.