As an example, let's say President Biden orders the FBI to prepare and release a report to the general public by a certain deadline. The deadline arrives but the FBI's employees either fail to meet the deadline or do a poor job. The head of the FBI explains that he did everything he could, but his subordinates were lazy and/or incompetent, so they couldn't get the job done. Could the President (or the head of the FBI) then decide to fire the employees involved for poor performance? In a US corporation the obvious answer is "yes" (thanks to at-will employment), but what about the Federal government?
Generally the president cannot, but an employee's direct supervisors can institute adverse actions of one form or another for poor performance. These can extend to dismissal, but missing a deadline would not lead directly to dismissal; most federal employees are protected by civil service regulations or similar provisions, so discipline is supposed to be fair and proportional, and employees are entitled to challenge wrongful disciplinary action.
The point of these regulations is to protect federal employees from being fired or otherwise improperly influenced by political appointees and, by extension, the president. If you are interested in learning more about these protections, you probably want to start with the United States Merit Systems Protection Board and the Federal Labor Relations Authority, both created by the Civil Service Reform Act of 1978.
Not currently, but it's (theoretically) within his power to change the law to do so.
Federal employees have Civil Service protections through the Civil Service act, but Trump, at the end of his term, issued Executive Order 13957 that gave the power to involuntarily move civil service employees to a fireable "Schedule F". The legal justification/theory is that the 3 branches of government are supposed to be separate and so a law passed by the Legislative branch (Civil Service Act) cannot constrain the head of the Executive branch from running the branch how they see fit.
Biden repealed that order as his first act and there's not a chance in hell he would re-instate it, but theoretically, he could.
Of course, there would be lawsuits and in practice it would depend on what the opinion of the majority of the Supreme Court decides about whether the Legislative branch can in fact constrain the internal affairs of the Executive branch like that, since it's not spelled out in the Constitution anywhere. Given the court's make-up, whether a conservative majority would rule for Biden, if it would help a Republican president later (or some Liberals could agree, since it's their guy asking for it), is completely up in the air IMO.