From: The Imperial Palace.
Seven homeworlds is a lot for a newb! And you probably were swarmed because your military wasn't as strong as that of your opponents. It helps to have allies, too.
As Malevolence said, try playing with a smaller galaxy, or maybe make colonizable worlds more rare, to cut down on the number of colonies you have to manage. I learned by starting with 1 world, 1 spaceport, and just a handful of ships, in a small galaxy. I put the game on slow, did everything manually, and slowly realized I could speed the game up without sacrificing my micromanagement. Now I can manage dozens of ships and several starbases, still with most things on manual.
Of course, I don't mean I'm steering every ship. I organize my ships into fleets, and I give the fleets orders like "patrol this system" (with range limited to that system). The minute a ship is built, I put it in a fleet, and it just takes its orders from the existing fleet orders. I order exploration ships to explore a whole sector of space, so they're busy a while. I use the UI to queue up construction projects at research or tourist worlds. I do queue up construction projects manually, but I don't find that to be a big burden. I revise ship designs manually too; I enjoy doing that.
I dunno, playing that way, I don't find it hard to keep track of everything. If 5 things happen at once, I just pause the game and deal with them one at a time. Mostly, though, I can run the game continuously while intervening frequently to give simple orders.