How do we perceive inner speech? Does it follow the same neural pathways as normal acoustic speech? If yes, what is the extent of overlap between the two neural pathways?
No, inner speech does not follow the same neural pathway as speech coming in from outside.
Rather, inner speech uses the same neural mechanism as outer speech - that is, speech going out. The neural mechanisms of inner speech can be studied using recently developed technologies such as fMRI imaging of subjects instructed to or prevented from engaging in self-reflection and internal monologue. Such studies suggest that inner speech is primarily localized to Broca's area (LIFG, on the left side of the brain), just as is outer speech (McGuire, 1996; Morin & Hamper, 2012). These findings are consistent with other evidence that inner speech is a form of silent (simulated) outer speech, and thus uses the same physical mechanism. This is based on private speech theories originating in the 1920s and 30s by Jean Piaget and Lev Vygotsky, that inner speech is actually outer speech that children learn to internalize.
However, if inner speech uses the same mechanism as outer speech rather than the incoming auditory system, then how is it that we "hear" it? One proposal is based on the attenuation mechanism involved in normal speech production. This mechanism filters self-generated sounds from other sounds. It is believed to work analogously to noise cancellation technologies - by predicting self-generated sound and modulating audio processing accordingly. Experiments by Scott (2013) and Scott et al (2013) demonstrate that this attenuation is also active in inner speech, and suggests that perhaps what we "hear" is the prediction of our own voice by this system.
Another approach by Alderson-Day et al (2016) distinguishes between multiple kinds of inner speech - monologic inner speech of the type traditionally studied as above, and dialogic inner speech that adds a second voice (an interlocutor). Brain scans of subjects engaging in dialogic inner speech show additional activity in areas associated with auditory hallucinations, and may therefore be "heard" in a similar way. This is still a very active area of research, so stay tuned!