Matt;
What my alter ego said
In the advent of TUL, the ARTCC site closest to it would be in OKC. So you can see that would be a little ways off.
The info is indeed sent via a type of modem and then merged into the approach control systems. Eroute radar is about half the speed of the terminal systems and rotates about every 10 to 12 seconds or so depending on the type radar being used. ( slow indeed <G>, it's what you get used to. )
As to the question about the pilots. You bet that we make some assumptions by voice and how well they use the radio. If they sound shakey we don't try anything other than the basics and don't try to do anything out of the ordinary to make them number one. We will just fit them in as best we can and watch them like a hawk
regards
Scott