You can put identical batteries in parallel, then the combination will last about twice as long.
No you can't.
They will cross charge and heat up.
That would not be putting two batteries in parallel, but in series and then shorting them. Two batteries in parallel is both positive terminals together and both negative terminals together. They can then supply 9V to the circuit for twice as long as a single battery.
And they only need to be the same capacity (Ah) and voltage; they don't need to be "identical". The same brand bought at the same time would be enough.