Within the federal court system there are how many basic levels ?

Answer 1

Three.

The trial courts -- including the federal district courts, the bankrupcy courts, and the other specialized Article I courts.

Then, above that are the federal appellate courts, and the US Supreme Court at the top.

A fourth "level" can exist below the federal district courts -- namely the administrative law courts. But that is not usually considered part of the court system, since it is run primarily by the executive branch as a quasi-judicial function.