I'm not familiar with the type of airbrush that you are describing, but it appears to be a cheap copy of general dual action airbrushes. 'Cheap' means that the o-ring seal that is called part 8 will probably deteriorate very quickly if it comes into contact with cellulose thinners. Its purpose is to form a friction seal between the needle and the paint-filled compartment forward of part 7, the trigger. If exposed to cellulose thinners it will have expanded to the extent that it no longer forms a seal.
This does not, however, explain your problem whereby the trigger just flops about. You need to ensure that part 13 is screwed fully home into part 6 and that the spring, part 12, is properly seated inside part 13. When part 14 is fully screwed onto the needle shaft via partr 11 it will grip the needle tightly, and you will be able to move the needle into and out of the nozzle by manipulating part 11.