Can't answer the fairing issue. I've seen some with it, and some without.
The oil light should indicate a certain amount of pressure. Cold oil is thicker than warm oil. So the pressure would be higher when it's cold. Warm oil is runnier, and needs less pressure to circulate around the system. It's possible your oil pressure sensor may be going bad, or perhaps there's some thinner oil in the crankcase. First thing to do is change the oil and filter using the recommended viscosity. Re-Run recommends a Rotella synthetic (do a search on the forum for Rotella to see it), and I think the factory service manual recommends a 10W40 non-energy-saving oil. If that doesn't resolve it, check to make sure your idle is at spec. I have mine set to about 1200, FSM says around 1000. If those two are ok, then the next step would be to replace the oil pressure sensor with a known good one. If _that_ doesn't do it, it's time to dig into the oil pump and see what's going on there. Let's hope it's the first 2 or 3 items.
$300 sounds like a great price for a neat project. I got mine as a birthday present from my family. Only cost them $500, and between tires and other little stuff, I have another $350 in it now. It's fun to tinker with.
I hope this helps.
Luke M
Used to have a 1979 CB750L, sold it as a parts bike, now riding a slightly modified 1984 VT700C. Network/Field Engineer. Central OH, USA, Earth, Sol System, Milky Way Galaxy, Universe.