As for taxes being "precise," that is an interesting claim. The US tax code is not even remotely precise, in fact it is hard to know what you are supposed to pay in taxes for the first paycheck of the year (your bracket could change unexpectedly). Our income taxes are progressive, but the wealthiest Americans pay little in income tax because their "true" income comes from their investments. We have the AMT which is meant to take care of that, but the AMT has not been properly adjusted for inflation and so a bunch of middle class families are stuck paying it, even though those families also pay income tax at a higher bracket than the wealthiest households that AMT was supposed to target. Then there are the countless things a person can get credits for -- children, particular kinds of business income, charitable giving, state and local taxes, etc. -- that result in people with the same income level paying wildly different taxes from their peers. Investment income is taxed, but losses can be carried forward, and some investments are taxed in a totally different way, some can also be carried backward (see Section 1256), etc.
On some level it is "precise," but in practice it is a mess that gets more difficult to work the more "established" you are in life (bought/sold a house? got married? have a new child in your life? finally made enough to contribute to a retirement account? get ready to do a bunch of paperwork to figure out what you are supposed to pay).
As for what the Fed is supposed to do, in practice, the Fed does much more than simply control the amount of money. The responsibility of the Fed is to control monetary policy and to maintain the health of the economy by doing so. Which is why they have such an important role, right now, in preventing the complete collapse of the US economy.
