Dynamic of 10 year UST given supply shock of the bonds that the Fed will buy into It looks like the US government are gonna issue a lot of bonds in the near future. Basic demand/supply implies that this will lower the price of those bonds i.e higher yields. At the same time it seems that the world is looking desperealty for dollars.

Hence where are all these dollars gonna come from if not the Fed? i.e the Fed buy all the bonds in order to one finance the deficit and two keep yields down.

What would be the long term effect of this kind of behavior?
Who will buys bonds; not including the FED

When a government wants to issue bonds, it will usually do so via a bond auction, where the bond will be bought by large banks or financial institutions. 

Those institutions will then sell the bonds on, often to pension funds, other banks, and individual investors.  So other banks and individuals also buys bonds. 

https://www.ig.com/en/bonds/what-are-government-bonds

other factors/actors pressuring up prices on these bonds.

If the economy is doing poorly (less economy growth) then investors might step back a bit from riskier investment and instead pile into government-backed Treasury’s, which pushes prices higher and yields lower.

https://www.investopedia.com/ask/answers/111414/what-causes-bonds-price-rise.asp

How does the dynamic of all this work with inflation? 

When inflationary pressures emerge, Treasury yields move higher as fixed-income products become less desirable. inflation eats into the purchasing power of every dollar you receive from bond interest in the future.

Additionally, inflationary pressures typically force central banks to raise interest rates to shrink the money supply. In inflationary environments, investors are forced to reach for greater yield to compensate for diminished purchasing power in the future.