How important is theory and research when policy makers write laws or make new policies? What role does theory and research play in policy making?

The answer to this depends on what kind of policy is being created and perhaps implemented. For example, a policy created that addresses an environmental issue would certainly require both theory and research. The lawmakers would (hopefully) have an understanding of environmental issues, the reality of climate change and humans' impact on global climate, and how the specific policy could impact the environment. If the Environmental Protection Agency wants to create a policy around limiting a coal company's pollution into a nearby stream, research displaying how that pollution is affecting the watershed or how the pollution of other similar company's pollution is affecting the watershed would aid in the creation of the policy. There will be clear numbers and expected outcomes for limiting this pollution.