Construction speed of colonies do depend on population. At least up to a limit. But the main reason builds on fresh colonies take ages and a half is lack of resources. You should get a warning if it lacks resources, you should see it on the colony if stalled due to lack of resources, and as long as the number of unbuilt components on the spaceport is updating, it is for sure not stalled right now...
As for the rest...
Mining: No, you should not build a mine on everything that moves. Look at your stores, sources, and unfulfilled demand in the expansion planner. Pay some attention to messages about shortages. If there are repeats, check stores of those resources in the expansion planner. If the shortage is on a major colony, pay very much attention to it. Fuel is where you want the most sources. Otherwise, look at the construction summaries of a spaceport and for instance destroyer, and a spaceport. You will see which resources are more in demand, and which you only need a small supply of.
In the expansion planner, the "resources by empire priority" should give an indication of what the AI thinks is most needed just now. Since the AI manages this all by itself if automated, it could be worth listening to.
Abandoned ships: Some abandoned ships are damaged, and must be repaired by a construction ship to gain control. This is true for one of the two ships in your home system, and you should be able to see which ones are damaged, and which are OK.
AI and Victory Conditions: Apart from the "difficulty scales as the player nears victory" option, the AI should not care about victory conditions. The races are configured to play according to their victory conditions, but they should not care at all about the "end of the game", or hunt the victory specifically.
Raid loot: I believe the raid loot is simply sent back through the hyper efficient pirate mail system. It is so efficient that it works almost instantly. How would a few escorts bring home thousands of resources, anyways?