The bank is not really owned by foreigners. The U.S. relies on other nations to buy our debts in the form of bonds and such through the Fed. It isn't really owned by anyone although banks may hold stock in the Fed. Stock in the federal reserve bank is different. It doesn't permit ownership qualities.
I learned the textbook definition of the Fed thanks to my econ minor.

The fed is the bank for the USA and therefore it is also the bank of banks. Basically, their job is to prevent financial panics. They regulate and supervise banks. They are supposed to keep things stable such as: interest rates(more specifically long term), high employment, stable prices(like inflation), economic growth through the use of monetary policy.
There is a board of governors who are top notch economists and Ben Bernanke is the chairman.
There are many areas of the fed that needs to be critically examined by those with bigger brains.
Politics and monetary policy is supposed to be separate but I think most of us know that isn't truly possible.
Why are the fed governors appointed by the senate and president?
Secrecy withing the fed.
The Fed doesn't let the free market work itself out by controlling supply and demand.
The perceived worth of the Fed is always being doubted and criticized.
The Fed keeps printing money at an alarming rate without plainly disclosing it to the public.
The Fed is the cause of the business cycle.
There is a lot to cover about this topic and a search would be much more beneficial.