What does the Fed do with their profits?
Fed sends its net profits to the US treasury. Fed keeps portion of the money it earns to cover its operating expenses but everything above that is necessary for it's functioning and dividends to member banks is remitted back to the treasury see the explainer by Fed St Louis here. 

For example, according to ABA Banking journal the Fed net revenue in 2018 was $\$55.5$ billion, from which $\$54.9$ billion was payed directly to the US treasury.  The dividend payments according the source totaled $\$714$ million, rest was all used to cover various operating costs.