It is always to a good idea the panel physician's clinic to call them and ask for an available appointment.
For my medical exam i was told i need to wait for 2 weeks. About the police certificate it is better you contact the address and telephones indicated by CIC. If it is close to you, you can walk in.
For the medical exam it should not take more than 1 or 2 days, for the police certificate you need to apply it in person, they will collect finger prints and will tell you when to come back for the certificate some countries will mail it to your home address.