How does sector 8 work?

I finally made it through an FTL game to sector 8 (on easy mode, of course), whereupon I found that everything changed.

Now I start at the right side, and there's a flagship on the left, and nodes are getting picked off one-by-one. I also was given some repair nodes, but apparently with no time to get to them before the flagship reached my base. (Later I discovered that the flagship doesn't move one node per turn, but only one node per two or three(?) turns.) Furthermore, I lost the game when the rebels reached my base even though the flagship was still a couple of nodes away.

How does sector 8 work? How fast does the flagship move? What conditions cause me to lose the game without getting blown up? (I realize this is more than one question, but I'm looking for an overall understanding of how sector 8 is supposed to work.)

Update for advance mode:

1. You start out on the left side of the screen, the rebel flagship is somewhere on the right.
2. There are repair points (and possibly a shop) scattered through the sector, as well as random battles with rebels.
3. The base is somewhere in between you and the rebel flagship. The flagship's goal is to jump to the base.
4. The flag ship makes one jump for every 2 of your jumps. The map will show the next node the flagship will jump to.
5. If the flagship reaches the base, it will take 3 consecutive turns to destroy the base before you get game over(thanks to BlackVegetable).

Old normal mode stuff:

Here is a rough breakdown of sector 8:

1. You start out at the federation base, somewhere on the right side of the map.
2. The rebel flagship is on the left side, and the fleet advances through the sector as usual per jump.
3. There are some repair points (and a shop) in the sector, and all random battles will be between you and a strong rebel ship.
4. There is a countdown timer at the bottom of the screen telling you how many jumps the rebel flagship has to make before its game over. As stated in that answer, the flagship jumps once for every two jumps you make.

5. The giant arrow leading out of the rebel flag ship points to the next sector it will be jumping to. It does not have to reach your base for the game to be over.

   6. The flagship has three stages, you have to defeat all three before the timer reaches 0 or you lose.