Check your colour photo licence - if it says 'aviation identification' on part II of the licence it means you can fly as pilot in command (i.e. go solo). This is known as an AVID. If you have this AVID you're in good shape - if not you need to upgrade your student licence to one. Speak to your chief pilot (they should be a CASA delegate) or CASA themselves about upgrading to the AVID. However, if you are under 18 you do not need an AVID to fly as pilot in command.
Regarding the medical, I am unsure about how much the extra 'processing' fee is, but I know there is one on top of what your medical examiner will charge. If no one around here knows, call CASA to find out. Next, get your medical ASAP. There is a delay in issuing these at the moment as well and you'll need a medical certificate to go solo.
If you don't have your AVID and medical certificate you cannot go solo, which will slow your training down. Allow at least 3 months for these, so get the paperwork signed ASAP.
Finally, you asked about an ASIC. You only need an ASIC if you are going to be going into security controlled airports. If the airport you fly at is security controlled, get one quickly (you'll need this to walk around controlled areas by yourself). If you are an airport that is not security controlled, you do not need an ASIC until at least your PPL training (when you will be visiting such airports).
To confuse things more, I believe an ASIC overrules an AVID. Therefore, if you do not have your AVID yet you may be better off applying for an ASIC.
If I am wrong can someone please correct me.
This was my interpretation of the rules - if I am incorrect someone will correct me.
Better still, speak to your flying school or call CASA on 1300 737 032 (be prepared to wait in a phone queue!).
