Hey Luke, yes your JAA licence will need to be completely current (including medical and LPC/OPC) before you can get an assessment from ASL. However once the assessment is complete, you don't need to keep your JAA licence current. The assessment lasts for a year. I've just been through all this myself.
With regard to the ATPL Law, the exams were recently re-written and as far as I can find out the sample papers were withdrawn until they could be re-written. I asked when that might be, and was told that it wasn't a priority and would likely be some time away.
I got all keen and wrote a set of study notes for ATPL law, basically just the syllabus items with the relevant rules and stuff reproduced below them. Still comes to 194 pages though! I can email it to you as a PDF if you want a copy.
Not sure what they will think about the Qatari licence but I wouldn't hold out much hope, ICAO or not. You can only get a type rating put on your licence if the type has been on the NZ register, which I doubt the A330 has.