- What temperature would the surface be?
Cold, really really cold, imagine the coldest winter you can remember, it's going to be colder than that, a lot colder, honestly it's going to be really cold, so cold you can't imagine how cold it's going to be.
Lets just say extra socks & a bobble hat aren't going to be much help.
- How quickly would it drop year to year?
Year by year? it wouldn't even take one year, assuming you start by moving away from the sun you'll be in a new ice age colder than any before it long before you get half way to the orbit of Mars.
- Would the atmosphere freeze, and if so, what would it look like?
Yes, it'll look like ice, what else would it look like.
- What would happen to cities, trees, the ocean, etc?
They'dThey'll all freeze.
Any other questions?
The only place you've any real possibility of life persisting for a bit is going to be in close proximity to an active geothermal of some sort. Yellowstone for instance might provide a haven for a few humans for a bit longer than elsewhere on the planet.