I wish I could tell you what the problem is... but I can tell you what it isn't and that is the oxygen sensor. The sensor has no part in the engine's starting because it has to be over 600 degrees F to function.

If one of my cars was acting the way yours is, I think I would examine the plugs immediately after the first cranking where it fails to start. Do you know how to read plugs?

On second thought, maybe I would eliminate cap and wire problems brought about by early morning condensation, before applying wrench to plugs. The backfire clue is another hint at a distributor cap and rotor failure. Either way, I would definitely examine the ignition secondary.
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Art Benstein near Baltimore