He was flying his CAG aircraft that night. BuNo 66168, was marked with "00" on both sides as per normal for CAG's bird at the time.
Don't know about the Felix emblem, as that was VF3, not VF6, nor if it carried victory flags, or the number. Suspect it did, probably 7 of them, his total. Being a CAG bird I would think it would be kept up to date on kills, as well as very tenderly cared for.
As a side note, the F4F he flew at Coral Sea had the side marking "F-15", between the national insignia and the cockpit.