Disclaimer: I am not a professional electrician.
1950s sounds kind of late for knob and tube wiring; I associate that more with the 1930s and before. By the 1950s, it was probably most common to use conduit, flexible armored cable (BX), or maybe the early versions of nonmetallic cable (Romex). Are you sure you don't have conduit instead? Knob and tube looks like this, flexible armored cable looks like this, and conduit looks like this.
If it's BX, and it needs to come out for some reason, about the only thing you can do is pull the whole wire and replace it with modern armored cable; you can't easily put new wires in the old metal armor. You may be able to use the old cable to pull in the new, so don't just wildly rip out all the old cable first. When you do get the old cable out, the whole pile may be worth a few bucks at your local scrapyard.
If it's really conduit wiring, the things I would look for would be rubber-covered wiring, and maybe rusty conduit. For a while, the insulation on individual wires was rubber, which tends to dry out and come off over the decades. Modern wire has plastic insulation, which doesn't go bad. The nice thing about conduit is that it's relatively easy to pull the old wires out and pull in some new ones. One thing to watch for - under older electrical codes, the conduit itself was allowed to serve as the ground wire, but now you're usually required to run a ground wire inside the conduit. If you have to do this, some of the conduit might be too small to handle the extra wire. Your local building inspector (city/county) will be able to advise.
A little surface rust isn't bad, but if the conduit has rusted through, you'll need to replace it. If the rusty spot is relatively close to a box, this isn't too bad, but if there's one rusty spot in the middle of a run, it can be a pain in the butt.
For the Cat6 outlets, you'll probably have to use electrical boxes that mount on the surface of the walls. You can get plastic or metal ones, and both kinds can be painted to match.
You *might* be able to drill a hole into the cinder block where you want the outlet, and another hole above that one at the top of the wall, and fish the cable through the holes in the blocks inside the wall. If that doesn't work, you can use conduit mounted on the surface of the wall. Regular conduit (the same stuff you'd use for 120 V) works fine, but for Cat6, you can also use flat plastic "conduit" - Wiremold, among other people, makes this. If you can run the flat plastic stuff in the corner, along the baseboard, etc, and paint it to match the walls, it doesn't look too bad.
Sometimes holes for pipes are a good place to sneak an Ethernet wire through. You want to stay away from things like the flue pipe for a furnace or dryer, but holes for the water or sewer pipes work fine. Then you just have to explain to the tenants why the Ethernet jack is under the kitchen sink or in the bathroom. :)