There's not a lot of detailed, explicit information about what actually is going-on with Morgan -- seemingly because of a bit of realism injected into the plot, since these scientists are still studying her and don't fully understand her abilities or limitations.
Morgan seems to be able to "see" people watching her through security cameras, and as you ask about, she seems to know things she couldn't know.
Ultimately, it's revealed that Lee is the result of a similar, previous experiment, but that in her design, they purposefully avoided emotionality and tried to target characteristics of loyalty, efficiency, and goal-driven sensibilities. This also isn't overly explained, but comes up quickly at the very end as the executives are talking.
The difference with Morgan was that they tried to ratchet-up "empathy" in her "design", and see if they could create this hybrid-human super-soldier that was even more self-reliant, adaptive, and capable. The executives talk about a feeling that the "Lee" design is good, but too cold and blunt and doesn't adapt very well, so they were trying to experiment.
Again, it's not really explained, but by reusing tropes from other movies (facing into a security camera like you can see who's watching, or knowing information you couldn't possibly know) they seem to be hinting at the idea that pushing for more "empathy" actually leaned hard towards "telepathy" and Extra-sensory Perception (ESP). They're basically suggesting that Morgan was still developing, but was becoming hyper-aware and actually verging towards reading minds, but it all seemed more instinctual than purposeful.
Since they get shutdown quickly, they never really got to explore where she was going with her evolution, so there's not a clear answer of where she was at.