For creating the pop-art style coarse halftone screens you see on some artwork, I would probably do that bit as a raster element in photoshop. Go into photoshop, create a greyscale document (you'll probably want to make it as high res as you can tolerate to get nice round halftone dots) and fill it with a gradient approximating the halftoned gradient in your artwork, then go to image>bitmap and for the bitmap method choose 'halftone screen', choose a round dot pattern and play around with the screen ruling settings to get a dot-pitch approximating the artwork you're trying to match (you'll probably need a really coarse screen ruling, 5lpi or something). This'll give you a 1-bit bitmap image where the dots taper away. You can place this in Illustrator, colour it up, crop it to a shape using masks, etc. If you want it as vector data you could load the document's only channel as a selection in photoshop and go to 'paths>make work path' to autotrace it, then export that path to use in Illustrator (it won't make nice geometric dots but you probably won't notice in the final printed output).
Failing that, you'd could draw a few of the biggest dots and a few of the smallest dots in Illustrator and use the blend tool (set to an appropriately small number of steps) to fill in the ones in between.
As for using the pathfinder divide feature to cut away the edges of dots protruding from shapes, it's probably a lot easier to just make a mask for your group of dots, so the edges are still there, but they're hidden by the mask - saves selecting and deleting each little dot segment...