Hi SoontobeinMelbourne,
I paid mine before I went and saw the DAME. Easiest way to do it is online. follow the link below.
Civil Aviation Safety Authority - Payment of fees FAQs
In terms of the additional tests, the eye test will be done by a DOA (Designated Aviation Ophthalmologist) so they will send the results to CASA directly. As for the blood test and ECG, They should be sent straight to your DAME but best to check with the people where you are getting the tests done.
Goodluck