A lot of dust and particles in the atmosphere is more likely to have a cooling effect by reflecting incoming solar radiation.
Oops re-read you covered this later in your post.
How long could it theoretically take for humans to live on the surface again? Are we talking five hundred years, or five thousand?
It would depend on the size of the particles, the smaller the particles the longer they would stay up there and affect the climate. My guess is that you would be talking years, rather than hundreds of years for the particles to sediment out of the atmosphere but the impacts may take longer to recover from. It would take a lot longer for the surface crust to redevelop, I 've no idea how long that would take.
- How would the world eventually look like? Would there be the same water/land ratio as today?
Your guess is as good as mine but if the impact vapourized a lot of water and threw it up into the upper atmosphere it would be photolysed. The hydrogen produced would be lost so there would be less water when everything cooled down and the water became liquid again.
- Where would the world be livable first? Would the earth's temperature be too high at the equator, or too low nearer to the poles?
The areas around the equator would get warmer first after the aerosol dust has settled. A lot of the variation in temperature between equator and poles is due to the angles and distances in the Earth/Sun system, unless the Earth's orbit has changed appreciably in the impact the same sort of variations would develop after the disaster.