Larsenex
If have tested your game save: By turn 219 the Iconians have colonized an additional three planets. They seem to be not building colonizers because they are rush buying combat ships and creating fleets. But the colonizers are being build eventually and used. The ship deployment is rather strange: Colonizer is build, goes to a fleet (i assume there is a rally point there), joins the fleet, and the next turn ejects from the fleet and goes to a colonizable planet and makes planet fall.
Everything behaves normal on my system.
Also the 13 seconds wait is not really excessively bad, on my system running a soak on your game takes about 9 seconds per turn. So it is the sheer map and data size that needs to be processed that gobbles cpu cycles.
On the approval: use approval buildings and starbase modules.
By the way to show images stored on dropbox you must alter the dl parameter in the url from 0 to 1.
If you use https://www.dropbox.com/s/bfhluh5ac1vew6x/2015-05-09_00004.jpg?dl=1 as the image source then your images will show properly.
