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.
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
Case law is based on the precedents and and legal principles applied by other courts in previous cases.
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).
Maple
federal and state.
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.