I'm just going to ignore rule #1, since I don't think the American Godzilla himself will be realistic, just the human reaction to the events of the film.
This is basically my idea of what the winged Muto in the film will be like, and is based on the assumption that it won't be related to the eight-legged Mutos at all (I just can't see any form of those monsters fighting like a bear or Komodo dragon, regardless of their size).
This monster looks something like the Keese from The Legend of Zelda: Twilight Princess in that it would be a bat monster with a hook like stinger on the end of a long, prehensile tail. When on the ground, it stands upright rather than on all fours, like Rodan, and stands just a little shorter than Godzilla. Like Otachi (the flying monster in Pacific Rim), it folds its wings almost completely into its arms when not flying so that you can hardly even tell that it has any. When in this standing posture, it really looks closer to a bear than a bat due to having very stocky features, like Godzilla himself. When it takes flight, however, it unfolds it's wings to an absolutely massive size, as in, its wingspan should be at least three times its height, and then jumps off the ground and powerfully beats its wings simultaneously, causing it to quickly take off at almost full speed.
A list of the monster's abilities and characteristics:
-Very resilient hide that is immune to conventional weaponry, but not nearly as resilient as Godzilla's scales and giving very little resistance to his Atomic Breath.
-Flight at Mach 3.
-A mutated form of echolocation that sends out soundwaves that travel and bounce back at supersonic speeds, so that it can still be useful when it is flying faster than sound.
-Claws hard and sharp enough to pierce Godzilla's hide at high velocities (e.g. when flying).
-Stinger on tail that injects a paralyzing venom into an opponent's bloodstream even if it doesn't pierce their skin.
-WEAKNESS: Eyes are very sensitive to light, enough that something very bright (such as Atomic Breath) shining very close to its face could blind it permanently. Luckily, though, its above-mentioned super echolocation would mostly make up for this... except that anything that isn't a solid object, like say, the light emanating from Godzilla's dorsal plates as he charges his Atomic Breath, would be invisible to him (hint hint).