I'm not sure when taxes became mandatory, but the ability of the Federal government to collect taxes pretty much comes from the 16th amendment, which I think was passed in 1913. There were taxes before this. Income taxes were imposed to pay for the Civil War, but I believe were cancelled after (not positive).
16th Amendment: The Congress shall have power to lay and collect taxes on incomes, from whatever source derived, without apportionment among the several states, and without regard to any census or enumeration.
To me, this means they have a constitutional right to collect taxes.
I may be wrong, but I don't think the IRS is part of the Fed. The fed sets monetary policy (interest rates and the like). I'm not really sure they have anything to do with taxes.
I'm not really sure if this is anything you were interested in, but here it is anyway. Keep in mind, the article you linked to is a speech from 1934. What once MAY have been true, may have changed.
Why not go to
http://www.federalreserve.gov to learn about the Fed?