Hi Demonic, giving Company of Heroes a Rest?
Planet income depends on type of planet. You usually start on a Terran planet which is the best, the other types of planets do not support as large a population as a Terran one. Upgrading infrastructure will increse population and in turn increase income. Also if you are TEC you can upgrade the max population Terran, Desert and Ice planets can support. I am not too sure about the other two races/
Pirates always raid the closest target usually and rarely bypass a system. Static as in 'shooting' turrets are bad their 'denial' area is relatively small and can be bypassed. Hanger defences are always the best as they can send their fighters/bombers throughout the whole planet.
Advent? Fights and Bombers, nuff said

Also, use abilities of umm, i think they are called Iconus Guardians very useful for fleet survival. The ability of the Progenitor Mothership is nasty as well, can't think of the name of the ability off the top of my head though.
Advent are very much the 'culture' race, using it to decrease income of the holdings of other players and causing planets to even go neautral. The advent building is special, it can switch between being a refinary or a trading post, so use it to bolster either metal/crystal income or to increase credit income. Only use them if the game passes or will pass the 1 hour mark, earlier than that, resources would be better spent elsewhere.
Don't know about replays sorry.
Have fun!