Why don't we hear all the processes in our body and what prevents us from doing so?
The issue here is with the definition of the word "hear". We do hear most of this, that is our ears actually pick up and transmit this sound. But we don't hear it in the sense that our brain ignores it and filters it out of what we are aware of. Only a very small fraction of all the sensory data that comes into the brain ever gets processed. The brain does something called sensory modulation it filters through all the sensory data and decides what is worth paying attention too. 

This happens at several levels, not surprising since we see these same levels of filtering in animals, as soon as you evolve sensory organs the ability to filter sensory information is an advantage. Some happens directly at the sensory organ, many have a threshold before a signal is sent. In the brain the reticular formation is responsible for much of it. But each sensory processing area also does some of its own filtering. Basically each portion of the brain contributes in some way. Attention and how it is controlled is greatly studied as it is central to how consciousness functions. A complete rundown of all sensory processing is tricky since some senses (like smell) skip some parts of the process, and there are so many ways it can be filtered. you can find a more detailed breakdown here.