Dynamic of 10 year UST given supply shock of the bonds that the Fed will buy into
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.