Adding the O2 is almost trivial if you are using the stock M1.3 wiring harness. Add a bung on the downpipes and clip the sensor into the harness. Per Paul and Don, yeah, the O2 is super important to making it run correctly. Otherwise the car will default to pig rich all the time and probably pull timing, because it has no feedback on combustion effectiveness. (so it defaults to 'safe as possible')
The 'fuel tank breather valve' or PCV is more an emissions control device. In the original implementation, it opens up the intake manifold vac to a charcoal canister hooked into the fuel tank. It sucks the evaporating gasoline vapor from the tank and lets the engine use it.