Inner dialogue is produced by generating language and not articulating. The understanding of language takes places in the left temporal lobe (Wernicke's area), while the production of language takes places in conjunction with your left frontal lobe (Broca's area) and motor cortex.

Inner dialogue is distinguished from external speech simply by monitoring external environmental cues, e.g. you see someone talking and know they're the one talking. More interestingly, inner dialogue is distinguished from imagining someone else speaking by self-monitoring, i.e. an awareness you are generating the speech instead of recalling someone else speaking.

This self-monitoring action is more complex. In schizophrenics, this self-monitoring system is thought to be disrupted, resulting in the perception of inner monologue as externally derived - an auditory hallucination of "covert speech".

The study linked above found involvement of the right superior temporal gyrus, the right parahippocampal gyrus and the right cerebellar cortex in flawed self-monitoring in schizophrenic patients prone to auditory hallucinations, but that's only important for the other neuroscience wonks. The interesting part is that the attenuated areas were all on the right side, whereas language is classically thought to be dealt with on the left side - with the notable exception of interpretation of prosody in the right analogue to Wernicke's. What this finding means is yet to be determined.

Now to address your other questions in a less in-depth fashion.

It would be difficult if not impossible to determine if other species have a true inner monologue because we are unable to communicate with them. We do know that similar areas as described above are active in primates, but we can't query them as to their perceptions of events.

The inner monologue is likely to develop on pace with actual speech production, so in the first two years of life.

Finally, the subconscious is not a well-defined term and subsequently not used much in actual neuroscience research.

Edit: Can't seem to embed the link for Wernicke's and Broca's area above, so here they are in ugly long form. TIL about escaping apostrophes. Thanks, trifolium.