Suppose that you had an onboard fracturing device that would split
water into hydrogen/oxygen.  Then you wouldn't need an outside air
source and the 'gas' tank would become a water tank that you could
heat for no particular purpose except for below 0 weather.

And how would you inject this mixture into the pistons (more correctly
into the combustion chamber)  and why would you want to?  That would
make it a diesel.

Fuel injected gas engines are in lean burn and with all the controls
to regulate fuel and ignition, you are as efficient as it gets as
opposed to  a carb setup.   Combustion only occurs in the cylinders
under pressure in the presence of spark.  When the spark goes out, the
flame goes out.   Find a way to keep a spark going for the lenght of
the power stroke and see the efficiencies escalate.  Also see the
tempratures rise dramatically.

There are enuff brains out there who are looking at possible ways to
do more with less that if this were a viable idea it would be on cars
now or at least announced for cars in (?) years.

Suppose that our fuel tank was very safe, and 100% safe from
explosions.

Instead of fuel injectors, why not heat up the fuel, and pump this
high pressure gaseous vapor into the pistons?  I would like to see the
gas tank heated - kind of like a pressure cooker.  And the escaping
gas vapor gets channeled into the pistons where it's further mixed
with air.

Currently, liquid gasoline is sprayed into the pistons.  From what I
understand, the finer the mist, the better and more thorough the
combustion.

Since the gaseous gasoline is the limit to how finely you can atomize
the gas, I would think that this is the most optimum way to put gas
into the cylinders.