Below a list of questions for which I'm quite far to provide an answer but that faithfully represent my daily activities.

Spatial basis of abstract cognition: How do we think about things that we cannot see, touch or hear? How do we represent the passage of time? How do we think about the past or plan the future? How can we represent other's people mids, desires and beliefs? How do we retrieve, maintain and manipulate information in our mind's eye? If some of this stuff remains a mystery, for everything else we probably build an analogical mental space, cognitive maps, conceptual gradients and mental lines.

Language and semantics: How do we make sense of words? How comes that meaningless strings of written signs or arbitrary sounds are related to concepts? How do we retrieve and manipulate conceptual knowledge? I think that spatial abstract schemas still play a role here, but it is not the all story. Ok, take some statistical learning, a bit of sensorimotor knowledge, compositionality quanto basta, shake recursively and serve cold with the opera omnia of Charles Sanders Peirce. This should keep you busy until I figure something out.

Consciousness: What is the difference between conscious and unconscious cognition? What is the role of consciousness in language processing and it relations with semantics? Why is Siri not yet conscious?