The Fed itself does not print anything that’s done by US treasury’s department Bureau of Engraving and Printing.
It is true that Fed decides how much money should there be in circulation through its monetary policy. This also includes ordering treasury to print notes and mint to mint coins although it is worth noting that only small fraction of all US dollars are actually in this form. Most money is created through the fractional reserve system by setting the federal funds rate - a rate at which private banks can borrow money from Fed, and also reserve requirement (although that one is traditionally not used as a policy tool).
It is also true that Fed purchases government bonds and that this is one way how it creates money when governments itself needs them.
The interest rate on government bonds is set by supply and demand. The supply is controlled by the US government issuing its own bonds and demand is created by people or organization wanting to put their savings into these bonds.
The interest rate on these bonds gets smaller if there is high demand for them and vice versa (ceteris paribus). In fact one of the reason why Fed buys government bonds instead of just ordering treasury to directly print money for the US gov. is to create extra demand that lowers borrowing cost of US government.
Also, you should know that all profits Fed gets from the bond interest payments and also other activities are sent to the US budget, or to be more precise Fed sends all its profits to the US treasury which then adds them to the budget, so although Fed technically charges US government that interest it then pays it back to the budget so it’s just juggling the funds around in that case.