OP; That actually looks almost like a front brake which just happened to end up with the washer set intended for a rear brake on a bike with a round tube style brake bridge. If it was for the front, the curved washer/spacer would have a larger radius to match up to the fork better.

1) Since you have the brake as it is and you have a flat plate style break bridge, relocate those special rear washer/spacers to the parts bin as you don't need them here.
2) In past ages one could sometimes buy a replacement center bolt for a broken one or to refit a front to rear or rear to front. Probably not today through. I wouldn't bother chasing it.
3) Yes is is possible to thread the bolt down further, but many are hardened and chromed making them tough to cut with a threading Die. Seems more trouble than its worth unless you already have a set of dies and know how to do the job.
4) So you basically need to add a "really thick" spacer or a stack of washers to take up the extra shaft length. These are hardware items and an inch worth of them should be about a dollar US. If you can find them, special washers which are larger in diameter while still having a small center hole would be ideal to spread the clamping force. These are generally called "fender washers" and will often be a bagged item vice ones that would be in a bin on the shelf. Just ask the store help for some 3/16" fender washers (or the metric size if so inclined).
5) As long as you don't shorten up the housing so much that it binds the brake movement, the brake couldn't care less if the install is top or bottom cabled. For some models the bolts that hold/stop the housing and the one that do the cable clamping can be swapped to do the job. Consider if the ones from the old brake can be applied to the new one (if so buff them up to make the match better)...
6) If you can, you might want to switch to a rear rack with a different mount to get it out from under the brake bolt as the rack will try to sway under load and in turns which can break the bolt or cause it to loosen over time. Even on a frame without rack braze-ons, most modern racks can be mounted easily using P-Clamps (more correctly called Adel clamps). Get the ones with a rubber or nylon sleeve to protect the frame. At most hardware stores and auto parts stores.
7) Last tidbit; The lower quality caliper brakes used on the rear can tend to shutter, vibrate and squeal as the braking action bends the arms towards the front which then pivots the pads off the rims a bit letting them release and jump backwards to re-stick and repeat... It is simple to avoid by simply mounting the rear brake backwards (i.e., on the other side of the plate). That way both the front and rear brakes take the same toe in magic in the same way and all braking energy is trying to stretch metal in the arms, which is much harder than bending it. This is far from obvious, but give it a try! I have never seen it fail to really improve braking (on top of the line brakes like a Campy, it won't matter as those have very, very stiff arms).

Hope that helps some
/K