Precedent (an decision made by an earlier, often higher Court in a mostly or completely similar case) in most countries is a strong indicator for a judge how he should decide in a case brought before him.
Lower courts do not department from precedents, they must follow the rulings of higher courts. Lateral courts have precedent that is not binding and does not have to be followed.
Case law is based on the precedents and and legal principles applied by other courts in previous cases.
Supreme Court
None. US District Courts do not establish binding precedents.
Yes, if appropriate precedents exist for the case before the court. The US Supreme Court sets binding precedents, meaning lower courts are required to adhere to them (but don't always do so) under the doctrine of stare decisis (Latin: Let the decision stand).
Precedents
The decisions are called precedents. Precedents are used as a guide by future court cases with similar fact patterns.
None. U. S. District Courts do not establish binding precedents.
Precedents are the decisions in cases in the PAST. These past cases are used and applied to cases in the courts to provide certainty and consistency in the system of law and justice (no matter what legal system this is regarding).
There is no court that supervises all other courts. You may be confusing supervision with the lower courts' obligation to uphold precedents set by the US Supreme Court. The Supreme Court doesn't "supervise" them, however.
There is no doctrine of non-binding precedents. Non-binding opinions that may be used as guidelines for deciding future cases are called persuasive precedents. Binding precedents are upheld under the doctrine of stare decisis (Latin: Let the decision stand).
A precedent is an earlier action or decision used as a guide or model in future decision-making. Courts often use precedents set in earlier cases to render a judgment, under the doctrine of stare decisis (Latin: Let the decision stand), a common law principle.