That's quite an expensive (looking) frame. If you don't know what you are doing, it wouldn't be a bad idea to have someone more experienced do the work for you.
1)
Cane Creek SCR-5 or
Tektro RL340 are the standard choices.
2) Use zip-ties or clip-on cable guides (like
these) and run full housing. Cable stops are something else, which you don't need.
3) R538 should be fine. Before buying, you should measure the distance from the brake hole to the rim surface just to make sure the reach is correct. Different frames require different length brakes, and your frame looks short reach.
See here for how to measure.
4)
Sheldon Brown and
Jobst Brandt got you covered on wheelbuilding. There are plenty of 135mm single speed hubs, if you want fixed as well
Surly is a good choice. You can space out 120mm hubs (like the one you already have) to work, but that is a lot of space, and as a big guy, there's a good chance you might bend an axle.