The answer to this seemingly simple question isn't really so simple.
Is the Federal Reserve privately owned?
In reality, no it is not. It is setup similar to a private corporation, but the "shares" of a Federal Reserve district bank do not confer any rights of ownership to the holders beyond their par value and the right to elect SOME of the board members of the district bank.
The Federal Reserve system is setup in accordance with LAW. That law can be found in Title 12, Chapter 3 of the U.S. Code. http://www.law.cornell.edu/uscode/html/uscode12/usc_sup_01_12_10_3.html
Careful reading of that law can explain the Federal Reserve, but I give a brief synopsis.
The leadership of the system is provided by the Board of Governors of the Federal Reserve, also known as the Federal Reserve Board or the Fed. The board consists of the seven governors, appointed by the president and confirmed by the Senate. Governors serve 14-year, staggered terms to ensure stability and continuity over time. The chairman and vice-chairman are appointed to four-year terms and may be reappointed subject to term limitations.
The Board also exercises broad supervisory control over the financial services industry, administers certain consumer protection regulations, and oversees the nation's payments system. The Board oversees the activities of Reserve Banks, approving the appointments of their presidents and some members of their boards of directors. The Board sets reserve requirements for depository institutions and approves changes in discount rates recommended by Reserve Banks.
The Board funds its operations by assessing the Federal Reserve Banks rather than through Congressional appropriation. This to maintain its independence from political influence. Its financial accounts are audited annually by a public accounting firm, and these accounts are also subject to audit by the General Accounting Office.
A network of 12 Federal Reserve Banks and 25 branches make up the Federal Reserve System under the general oversight of the Board of Governors. Reserve Banks are the operating arms of the central bank.
The Reserve Banks serve banks, the U.S. Treasury, and, indirectly, the public. A Reserve Bank is often called a "banker's bank," storing currency and coin, and processing checks and electronic payments. Reserve Banks also supervise commercial banks in their regions.
National banks, like Bank of America, N.A., are required to become member banks of the Federal Reserve system. To be a member bank, a bank must "subscribe" to shares of a Federal Reserve district bank. Unlike shares in a normal public corporation, these shares cannot be sold, traded, or even given away. In fact, the number of shares a member bank subscribes to is set by the Federal Reserve Board as a percentage of the member banks capital. I believe that is currently 3%. So, if a member bank has paid-in capital of $1 billion, the bank would have to subscribe to $30 million of Federal Reserve stock. The value of the stock is set to $100 per share and the value does not go up and does not go down. To compensate the member banks for the loss of revenue this amount would have generated, Federal Reserve district bank shares pay an annual dividend of 6%. Approximately 38% of the over 8,000 commercial banks in the U.S. are member banks of the Federal Reserve system. BTW, the number of shares in a Federal Reserve bank is flexible. If a new national bank was incorporated, the district bank would simply issue more shares to account for the new "subscription" of the new bank. The value of shares in the district bank would not change. As I mentioned, national banks must be members and state banks may become members if they meet certain requirements. The key to distinguish between the member banks owning the district banks and whether the federal government does is which would get the assets of the district banks. The member banks would only receive the amount of money they paid to subscribe to the shares. Any excess assets above that amount would revert to the U.S. Treasury. That is your answer.
Does the Federal Reserve rebate net revenues to the U.S. Treasury?
Yes, it does. This can be seen in the INDEPENDENTLY AUDITED financial statements of the Federal Reserve Banks. Anyone who says the Federal Reserve has never been audited, didn't look very hard. The audit reports are part of the ANNUAL REPORTS to Congress. The following is the link to the 2006 annual report.
http://www.federalreserve.gov/boarddocs/rptcongress/annual06/default.htm
Audits of the Board of Governors and Federal Reserve Banks can be found at http://www.federalreserve.gov/boarddocs/rptcongress/annual06/pdf/audits.pdf
On page 3 is the independent auditor's report on the financial statements of the Board of Governors. The financial statements and notes follow that report.
On page 21 is the independent auditor's report on the combined financial statements of the Federal Reserve Banks. On page 23, the statement shows a $29 billion payment to the U.S. Treasury.
Do all banks create money out of nothing?
In simplest terms, yes. This is because of fractional banking. When a person deposits money in a bank, the bank is allowed to make a loan to another person based upon the amount of money on deposit less a small amount held in "reserve". If you want to know exactly how much money in federal reserve notes (dollar bills) is actually circulating, it can be found on the financial statements of the Federal Reserve Bank too. On page 22 of the audited statement, under liabilities, it shows there are a little over $783 billion in Federal Reserve notes outstanding.
Have inflation rates been lower and more stable in the last 30 years than most of history?
Debatable, but the Federal Reserve has for the most part since the mid-1930s, done a fairly decent job controlling inflation.
EDIT: Article 1, Section 8 states, "The Congress shall have the power...To coin Money, regulate the Value thereof, and of foreign Coin, and fix the Standard of Weights and Measures;..."
Article 1 Section 10 states, "No State shall...coin Money; make anything but gold and silver a tender in the payment of debts." This is a limitation on STATE power, not on the power of Congress. Congress can make money out of anything it wants to.
Why are there only 12 locations? Because at the time, and mostly still are, the financial centers and most business were located in those areas. There doesn't have to be 50 Federal Reserve Banks, there is no need.
What does the 13th amendment have to do with the Federal Reserve? The 13th amendment concerns slavery. So you think it wasn't properly ratified? Do you tell all of your African-American friends that slavery is still constitutional? If you meant the 16th amendment, that doesn't have anything to do with the Federal Reserve either. The 16th amendment concerns income tax. The 16th amendment was properly ratified, but even if it wasn't, precedence and 90 years of court cases say it was. Therefore, it is now a part of the Constitution and it will take another Constitutional amendment to remove it.