QE is revenue neutral in theory just like helicopter money along with taxing that same amount back on a future date is revenue neutral in theory. In practice it is more like "buy $4 trillion worth of assets with created cash and never be able to sell it for fear of creating a liquidity crisis": https://fred.stlouisfed.org/series/WALCL.
And they buy assets at whatever price is required for the financial institution to remain solvent. At least, that's what happened during the mortgage meltdown.