How to locally install .deb without apt-get, dpkg or root access?

You can download the source for python-2.7.10 from the python.org site. Once you extract .tar.xz archive you will find the Include directory that contains the missing missing header files.

You can tell python setup.py ... to look in this directory as well by setting

export CPLUS_INCLUDE_PATH=/path/to/your/extracted/Python-2.7.10/Include