Trump does not have the authority to fire or replace any Fed member if they have not violated the Constitution and their term has not ended. He also has no say in choosing who becomes a new Fed member or Fed chairman. He only has the right to nominate candidates but the decision rests with the Senate.
Also, he may have close relationships with members of the Supreme Court, but he does not control them. Likewise, the Fed has 11 members and the rate hike/drop is based on voting results, he will not be able to interfere, let alone control the Fed.
The Fed is an independent institution and its mission is to maintain the strength and dominance of the dollar, not just the US economy.
That's right, regulatory wise President Trump cannot replace Fed members at will. However, I think Adriana Kugler resignation is part of a scenario that gives Trump room to place his trusted people on the board chair. I think Trump, with all the authority and influence he has as president, can do anything to realize his plans. Ultimately, the Fed may have to follow Trump wishes to lower interest rates.
As I said, the Fed's job is to maintain the strength of the dollar, and that is the core of American strength. That is why the Fed needs to be independent of the US government and avoid being politicized. If Trump can politicize the Fed, it means the world's confidence in the USD will be shaken and collapsed, and US dominance will also disappear.
If the Fed is politicized to serve Trump's political purposes, the consequences will be huge and I believe Congress is well aware of that and they will not let that happen.
Update: Trump has ordered the firing of Fed Governor Lisa Cook on unconvincing charges. That's why she said she won't comply, and what can Trump do? Trump can do nothing, and the case will soon go to the Supreme Court, the only place with the authority to decide.
https://www.nbcnews.com/politics/white-house/trump-removing-federal-reserve-governor-lisa-cook-rcna227138