Can my boss request a doctor's note with the beginning date, diagnosis, prognosis and expected dates of return?

They cannot ask for a prognosis at all. They can ask, not for a detailed diagnosis, but for a simple description of the issue, both to confirm it is "legitimate" and that it is a justified absence. They can also ask, so that they can know if it may affect your job, or pose risks to coworkers or customers. And they can ask for an expected return date for their planning purposes.

What your employer is asking for is partly legal. There are various laws, at both the state and the federal levels, which protect an employee’s rights to medical privacy and which also prohibit discrimination against an employee due to his or her disability or medical condition and which therefore indirectly preclude the employer from inquiring too deeply into medical issues (since if the employer does, and there is subsequently some negative employment action taken against the employee, like suspension or termination, it could easily be construed or found that the negative action was due to the disclosed medical condition).

However, while the employee has legitimate privacy rights in this regard, the employer has legitimate rights and interests, too related to running and protecting their business. An employer’s primary interests are: 

    • To make sure that the claimed medical absence is legitimate. Remember, there is no general right to time off from work, so the employer can verify that the requested absence is actually related to a medical issue. They do not need to take your word for it -- they can request proof.
      • For planning, scheduling, workflow, etc. purposes. The employer has work that has to get done. They cannot plan for who will do it or how it will get done without knowing how long you will be out. Only by knowing this can the employer determine, for example, if they have to hire a temporary worker (and if so, for how long) to do part or all of your job.
      • To make sure that even if it is a legitimate medical absence, that you are entitled to the time off. Even for medical purposes, you can only miss work a) if you have and use paid time off (like sick days) you earned, which means you can’t miss more work than you have sick days; or b) if the company and you are both covered by some medical leave law (like FMLA), you can’t miss more work than the law permits (12 weeks of unpaid under FMLA and most similar state laws).
      • To make sure you don’t pose a risk to yourself or other people while working. If you have a condition which will make driving dangerous even after you return, but driving is part of your job, your employer is entitled to know that. If you have a condition that would make it risky for you to handle, say, food, but you work in a restaurant, the employer may know that, too. You can undoubtedly think of other examples as well.

So the employer cannot inquire in the details of your condition or prognosis, but is entitled to verify that you have a medical condition; to know how long you are anticipated to be out; and to know if, given the nature of your job, you have posed a risk or will pose a risk on your return. Your employer can seek medical verification of facts related to these legitimate business interests.