No the Fed doesn't give the Treasury green notes. It gives Treasury electronic digits in its account. Those digits are then also in the Fed's "reserve" upon which the entire banking system gets the power to inflate the money, i.e. based on fractional reserve banking create electronic digits in corporate and personal accounts (make loans, i.e. create digits, and collect deposits, i.e. create digits, over and over again). The green notes are only pumped out of the banking system when somebody asks for them...from a person or an ATM and they typically are quickly sucked back into the banking system as soon as a person uses the bills to buy something. They are printed by the Fed, not the Treasury.
Sorta and sorta not. The problem is you're assuming real economic output, i.e. all growth is coming from a bunch of Henry Fords generating ROI. That would be a production-based economy. However, we have a consumption economy where faux growth comes (at least before the crash) mostly from inflated credit, i.e. purchasing power generated by the banking system's ability to keep inflating (give people more purchasing power) based on expanded reserves at the Fed. The reserves are based largely on Treasury debt, and therefore, yes, you're correct in this type of economy the government will always be in debt.
Our economic "growth" is no longer driven by companies like Ford as much as it is generated by companies like JPMChase, Bank of America, Citigroup, Goldman, Morgan, AIG, Merrill, Countrywide, Fannie, Freddie, etc. as they continue finding ways to further inflate credit and shift money back and forth which makes it look like "growth." As of Sep 08, we know that "growth" was largely an illusion. And if the finance industry wasn't in bed with government, it would be called fraud. And in response our government has stolen even more trillions from the productive economy to hand it over to these fake "growth" financiers. Twilight Zone...na na na na...na na na na...na na na na...

If we assume that there are four people in this world - A, B, C, D.
A Cooks food.
B Makes clothes.
C Washes clothes.
D Makes shoes.
For a long time society has lived happily doing just the basic things bartering each other services.
Then came coins, then came gold coins. Lets suppose A, B, C, D each has 10 gold coins each and they exchange 10 gold coins for each service. Ultimately, each one is left with 10 gold coins.
There is no more gold in the world, so gold cannot be mined. Hence the govt. takes the 40 gold coins and prints 40 dollar bills and gives 10 each to A, B, C and D. Instead of exchanging gold, they now exchange dollar bills.
Now, Henry Ford comes along and makes the automobile. That is real economic output and everyone wants to buy a car. The government increases the Money Supply commensurate with economic output (gdp growth). As there is no more gold that can be mined, the govt creates new notes for the economic output.
That part is clear to me.
I don't understand how it is done!
The treasury issues bonds, and the fed buys the bonds and gives the treasury the green notes, and the government distributes the green notes to its contractors/suppliers and they wound up in bank accounts and due to fractional reserve banking the supply increases?
So, as economic output increases, government issues T-bonds to increase money supply? Is that it in its simplest form? If so, the government will always be in debt. Obviously, I am not getting something!