Turning a mobile home with a basement into a recording studio
Not knowing what you have for head space under this mobile home and what the moisture/humidity levels are, makes a difference.  Let us assume, for the purpose of answering the construction questions that the space is tall enough and dry enough to use as a functional  space. Notice that I did not say living space. Most codes would require minimum ceiling heights, egress etc to be considered living space.

Most single wide MH's are designed to sit on a slab or jacks/blocks on a slab. Not knowing exactly where these walls are located under the MH may be a clue as to whether or not they are supporting the floor above. If there are beams that span the 12 foot width and rest or are welded to the parameter frame then the load may well be supported by the outside beams. If there is a center main beam  at apx 6 foot, that well may need to be supported at some point along it's length. You may need to do some research into the manufacture's spec for placement.  Without actually seeing the construction of the existing walls, their placement and attachment to the upper floor, it is unsure what their purpose is. A few strategically placed jack posts may be required to replace the existing walls if the center line of the MH needs support. 

The other requirement is that the plumbing is protected from freezing. If you remove insulation from areas of plumbing, then it may be necessary to heat the area to avoid freeze ups. Also, the temps inside the MH could be effected by removing insulation from the underside of the floor.