Answer 1:
1.- I am envisioning a set of LCD panels arranged into a hollow cube. LCDs use pairs of glass panels sandwiching a liquid crystal mixture, so a filled cube could be possible with thick layers but it would still only rotate light that enters from one direction. An LCD would only rotate the oscillation plane of the light. This occurs because successive liquid crystal layers of the LCD assembly are at small angles to each other and gradually adjust the vibration direction from when the light enters the first panel until it leaves through the second. (Assuming the laser is not polarized at 90° to the incident side of the LCD, as the laser would not be able to pass through the first piece of glass if that were the case. This is simply how light polarizers work .)
The fact the light would be coming from a laser should not affect the function, nor should the LCDs being arranged into a cube. However, flat LCD panels do not deflect (refract, change propagation direction) light in a coordinated way like lenses or mirrors do. In projectors, both LCDs and lenses are used, but they are separate components. ("Deflecting" light by randomly scattering it with LCDs could still have uses though, such as protecting against laser pointer attacks on airplane pilots.)
More here.
2.- LCDs are used for image display, not image capture, so I'm not sure how this is directly related to the LCD cube and part 1. Regardless, lenses could be arranged like insect compound eyes to capture a wide field of view in a single device. At least one group has accomplished this, with essentially a large array of single lens/sensor cameras attached to a hemisphere. It seems to function like real insect compound eyes, such as maintaining focus when the object is moved nearer or farther.
[There are few examples of this technology in the news, but here is a lengthy recent academic article describing the current state of the research.]
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