I would stick to their thinner, or Testors thinner... maybe some other Aztec owners can give you a better answer. I would hesitate to use lacquer thinner in it as of all the plastic... I'm not famiiar with the brush cleaner, is it for airbrushes or regular brushes? If it is for airbrushes I am sure you can use it as well...
I would definitely soak the tip for awhile after you are through spraying(I used to do it overnight on my old Aztek) to make sure you get all the crud out.. Many people run into gradual buildup of paint in there till it clogs...
Maybe one of the Aztek users could tell you if you could use mineral spirits which I am thinking you can... much cheaper to clean with and even thin paint with!!!