Should I cut-in the whole room at once, or only the portion I'm working on?
It really shouldn't matter. In the end, it's the exact same paint so it should match. 

What can cause the halo, though is if your brush vs. roller technique lay down different amounts of paint. In my experience, it's easier to lay down a thicker coat of paint with a roller than brush, so after doing one coat of cutting in, and then one coat of rolling, you may notice the edges look lighter because there is less paint there. That said, I've yet to find any magical wall paint that only takes one coat so by the time you get the second (or sometimes 3rd coat) on you shouldn't notice it.

The only reason you may not want to cut in well before you roll is if you want to reduce the amount of brush marks as much as possible. While the color won't change based on what you are using, the texture may. 

What I typically do is do them both at the same time. I'll cut in around a window, then roll as close as I can get safely with the roller to even out the texture. Then I'll cut in the ceiling on the same wall, then roll that, repeat. 

Also, if you just hate cutting in, or have so much to do it's daunting, consider not doing it all at the border of the ceiling and walls and instead roll close to it, then when finished, tack up some crown moulding. It doesn't have to be fancy moulding at all...even a 2" bit of slightly tapered door casing can look sharp. 

That's the technique I usually use on already painted rooms that I'm repainting. Often the previous paint job at the border is just sloppy enough that even if I carefully go to the edge, there's enough spots of the old color that creep out that it just looks tacky. In those situations I go get the pre-finished window casings from Home Depot (can be found for less than a dollar a foot) and tack them up with a brad nailer. For a slightly more modern look you can use plain dimensional trim (such as a 1 x 2).

Yet another technique to avoid all that cutting in at the corner of the ceiling and wall is to simply paint them the same color. I'm redoing a bath that needs new paint on both the walls and ceiling so I'm going with a very light gray for both.