You cannot chose the biometrics appointment date, time, and location. After your I-485 adjustment of status (AoS) application has been filed and you have a receipt date and receipt number, then in ~2-4 weeks you will receive a letter in the mail from the USCIS with your biometrics appointment (stating the date, time, and location). In other words, yes, the USCIS assigns you a date, time, and location for your biometrics appointment.
If you call the USCIS after you receive your biometrics appointment to ask to have it rescheduled, then they will assign another data and time, but you still do not get to choose it. Also, rescheduling your biometrics appointment only serves to delay adjudicating your I-485 AoS application.
You need to make whatever arrangements are necessary so to go to your scheduled biometrics appointment. (As an example, for my daughter she had to reschedule an university exam, and I drove the 2 hours to pick her up from school and the drove her back after our biometrics appointment.)