Though most health insurance companies do have premiums shown as a per week ammount, normal thing is to pay monthly, or for longer periods of quarterly or annually for a small discount.

For the application and a need to have health insurance a letter showing you have signed up for a policy may suffice but do confirm it with a PLE via the contact tab on Immi site pages.

With the english, looks to be a five year study period the're looking for to get given an exemption.
Skilled Workers Temporary Visa Options - Employer Sponsored Workers - Workers - Visas & Immigration