In regard to how long it will take for payments to begin, you will have to wait for a final ruling from the court.
In regard to back payments, at the very least, I would expect payments to be ordered from the date of the test or the date that the very first application was filed with the court. The court however does have some discretion in this area and may order that payments begin from an earlier date, but that would be decided on case by case basis. There's no way to know beforehand if the court will actually make such an order.