the assessments only come after you have started your training, you don't need to pass any test to become a student pilot. as for the relevant paperwork, you will need an SPL, ASIC card and valid CASA Class 2 medical. apply for these ASAP, CASA is not especially known for its efficiency. make sure you get your SPL and medical certificate in time before your first solo - you cannot go solo without these.
i don't know about visas and immigration policy, but i'm sure that CASA is not responsible for this, you will have to check with DIMIA.