Director can do everything you're asking about - though I don't know what
dynamically loaded grids
However, don't bank on Linux ever being supported by Director.
I no Flash expert, but a lot of what you're asking I think is beyond the native capabilities of Flash - you might ask on a Flash forum also. Perhaps Director's greatest remaining strength over Flash is the ability to extend it with xtras (DLLs)
Air 2.0 can do everything you want straight out of the box and more. Forget about Director. It's ancient technology that is barely supported by Adobe.
I doubt you will need to write any DLLs, but if you do need to, you can create native installers for all three platforms and access dlls.
Neither Flash nor Director allow for threading, but it is not a problem. i.e., in Flash you would add an event listener to your Http service call object and your program will be notified when the data is ready.
You may want to use the Flex framework. On this site there are three videos that introduce how fast and easy it is to work with the Flex framework among many other useful tutorials: http://gotoandlearn.com/index
For a quick tour of what you can do with Flex take the Tour de Flex: http://www.adobe.com/devnet/flex/tourdeflex/
I suggest you use FlashBuilder to do your development work. http://www.adobe.com/products/flashbuilder/