I'm going to assume that you live in a state that doesn't require vehicle inspections. If you do, don't pull the cat. It's a Federal requirement, not state, which means that it's required in the U.S. Technically, you can get a ticket for it, no matter what state you're in, but if they don't inspect, they'll probably never know.
As for your other question, I believe that the O2 sensor just stays on the one manifold, even with dual exhaust. The routing of the exhaust after the headers doesn't really have an impact on the air/fuel ratio of the engine (that I know of, at least).
Also, why go with long tubes? I'm looking into getting a set of Tri-Y's, and everything I've seen recommends them as the best headers for overall performance. Doug Thorley sells them for about $650, which is steep, but they're ceramic coated and really high quality. Just thought I'd ask and throw that out there. Plus, they also have the bung for the O2 sensor, so you don't have to mess with it.
Lastly, what made you decide on 3" tubing? Unless your engine is modified and needs the additional airflow, 2.5" exhaust is plenty for running dual exhaust. Single exhaust - sure, run 3", but since you have two pipes, 2.5" is enough. Going too big can affect backpressure and scavenging.
http://www.magnaflow.com/wideopen/performdata.asp
Take a look at the chart on the bottom of this page.