Is there a way for this MPS file with specific format to be read and solved?

Expanding a bit on Tristan's answer: your MPS file is nowhere near a file conforming to the MPS standard nor the extended MPS format used by Xpress.

I suggest to double-check the tool that creates this file and see whether it has an option to create a standard conformant file.

It is easy enough to shuffle and/or rename the sections in your file, but like Tristan said, the data inside the sections is in a bad format as well. For example, the XLINEAR section cannot be considered as ROWS sections since it not only specifies row sense and right-hand side, but also left-hand side coefficients.