My cocoa powder settles in the bottom of the mug when I make hot cocoa using half-and-half (the dairy product). Is there any technique to prevent this? 
Stir!  It's normal :-).  If you want a really smooth suspension, you won't be making it with real cocoa powder, or real dairy.  However I always make a paste with the cocoa and a bit of cold milk while the rest of it is heating up.  That gives the best texture to the final product.  If you don't do that, try it. 