1 & 2: It's to do with the relationship with demand. If everyone just stuff the money under the mattress, it's not going to bid up the price of stuff and therefore destroy the value of the currency already in circulation.
3: Austrian theory says there shouldn't be a central bank.
3(a)Interest rates should/would be determined by the supply & demand of savings & loans.
4: Well the simple reality is that inflation is calculated through a "basket of goods", making it an inherently engineered metric. Things which are not in that basket can head stratospheric (i.e be bid up) and the reserve bank is mandated to do absolutely nothing.
A very easily demonstrable example of this is housing - if you used house prices to calculate inflation, over the past 20 years or so you'd say inflation was on the moon.
Understanding things this way is how we can have what you might call "hidden" inflation. I.e that rates are too low and sending the price of stuff (like housing) soaring but because this isn't counted in the metric, we "don't have inflation".
What I'm saying is that it all depends on how it is calculated. You can flush the country with cash, the country uses it to do nothing but bid up the price of something not in the cpi, and so as far as the fed's concerned, there hasn't been any inflation anywhere, even though there actually might have been tons of it, it just hasn't been counted. Hence the ability to print money to eternity and, officially speaking, not have any inflation anywhere.