1) The sensorium is all the circuitry in your body that makes you feel : the sensory components in your brain, the nerves that lead to sensors : pressure and thermal sensors of the skin, chemical sensors on the tongue and in the nose, light sensors in the eyes, vibration sensors in the ears. Thus, the sensorium is your interface to the physical world.
2) Sensoria is the plurial of sensorium. Your body only has one sensorium, and it's not conceptual, it's just grammatical : if it had several sensoria, you could consider the sum of them to be your sensorium. Side note: I personally believe we can apply the same grammatical explanation to a lot of differences; for instance, the difference between monotheist and polytheist cult.
3) The movie Matrix is a fiction based on the fact that your sensorium actually interfaces with another system than the real world, and in this case, the 'other system' is a super-computer. Besides the salable sci-fi idea of a super-computer, the movie reminds us that we are not in contact with the reality, but only with an interface to the reality. This interface acts as a filter, and therefore is not enough to apprehend reality. As reminded by Descartes, the conscious mind sees reality better than the senses.
4) When dreaming, the sensorium is fooled. or is it? I remember hearing something like " I dreamt I was a butterfly, starting a dream it was a man; just when I woke up ".