You don't owe anything in federal income taxes. Federal income taxes were declared unconstitutional by the supreme court in 1895 and the decision stood until the 16th amendment in 1913 when they were declared constitutional and mandatory again.
During those years, the US didn't receive any money at all from it's citizens and because of this the US reserve started to decrease.
If you would owe them, however, they would be paid directly to the US Federal Government.
An Appellate Court is not (usually) the Court of original jurisdiction. So, in many cases you would start at a Federal Trial Court (District Court) and would have a normal trial. If you lost, you could appeal to the Appellate Court, who would review the record (only) from the Trial Court for clear error, bias, etc. A new trial does not occur at the Appellate Level, unless it is a court of original jurisdiction.
