Pip not working; from 'ImportError: No module named urllib3' to non-admin windows user - pip

Question

I am facing some problems with pip. The original error message in my command prompt (windows, Python 2.7.14 and this is the version I must keep) when typing for instance pip was
Traceback (most recent call last):
File "c:\python27\lib\runpy.py", line 174, in _run_module_as_main
"__main__", fname, loader, pkg_name)
File "c:\python27\lib\runpy.py", line 72, in _run_code
exec code in run_globals
File "C:\Python27\Scripts\pip.exe\__main__.py", line 5, in <module>
File "c:\python27\lib\site-packages\pip\__init__.py", line 21, in <module>
from pip._vendor.requests.packages.urllib3.exceptions import DependencyWarning
File "c:\python27\lib\site-packages\pip\_vendor\requests\__init__.py", line 62, in <module>
from .packages.urllib3.exceptions import DependencyWarning
File "c:\python27\lib\site-packages\pip\_vendor\requests\packages\__init__.py", line 29, in <module>
import urllib3
ImportError: No module named urllib3
My journey to solve/explore the problem:
This happend no matter which of the following prompt commands I was trying
pip
pip --version
pip list
pip freeze
pip install --upgrade requests
pip install urllib3
Other commands might have change the error message a little bit in terms of the files listed like
python -m pip install --upgrade pip
Traceback (most recent call last):
File "C:\Python27\lib\runpy.py", line 163, in _run_module_as_main
mod_name, _Error)
File "C:\Python27\lib\runpy.py", line 111, in _get_module_details
__import__(mod_name) # Do not catch exceptions initializing package
File "C:\Python27\lib\site-packages\pip\__init__.py", line 21, in <module>
from pip._vendor.requests.packages.urllib3.exceptions import DependencyWarning
File "C:\Python27\lib\site-packages\pip\_vendor\requests\__init__.py", line 62, in <module>
from .packages.urllib3.exceptions import DependencyWarning
File "C:\Python27\lib\site-packages\pip\_vendor\requests\packages\__init__.py", line 29, in <module>
import urllib3
ImportError: No module named urllib3
I have checked the following (according to several suggestions I found in related questions on stackoverflow)
a pip application can be found in C:\Python27\Scripts
dont have something called PYTHONPATH in system variables only Path
C:\Python27\Scripts is listed in system variables>Path
anaconda was installed by the user before me. I uninstalled as apparently this could cause troubles and deleted all remaining .condarc files,./conda & conda folders as well as the system variable>Path listing.
I have tried the solution which was voted for here by downloading and running python get-pip.py. This is the error message:
>python get-pip.py
Traceback (most recent call last):
File "get-pip.py", line 23974, in <module>
main()
File "get-pip.py", line 188, in main
tmpdir = tempfile.mkdtemp()
File "C:\Python27\lib\tempfile.py", line 331, in mkdtemp
dir = gettempdir()
File "C:\Python27\lib\tempfile.py", line 275, in gettempdir
tempdir = _get_default_tempdir()
File "C:\Python27\lib\tempfile.py", line 200, in _get_default_tempdir
with _io.open(fd, 'wb', closefd=False) as fp:
AttributeError: 'module' object has no attribute 'open'
I was told there were some problems noticed before: The computer has 2 users, an administrator and an additional user with '(user)' in its name. I was told that it was not possible to install anaconda for that user - it was installed by the administrator for all users but in the end spyder for instance and the anaconda prompt could only be ran as administrator, too. So I am not sure if there is a problem in general with the user setup?!
I ran the command prompt as administrator and pip --version worked
pip 9.0.1 from c:\python27\lib\site-packages (python 2.7)
So I ran python -m pip install --upgrade pip as administrator, opened the command prompt again (not as administrator and now the new error is
Traceback (most recent call last):
File "c:\python27\lib\runpy.py", line 174, in _run_module_as_main
"__main__", fname, loader, pkg_name)
File "c:\python27\lib\runpy.py", line 72, in _run_code
exec code in run_globals
File "C:\Python27\Scripts\pip.exe\__main__.py", line 5, in <module>
File "c:\python27\lib\site-packages\pip\_internal\cli\main.py", line 10, in <module>
from pip._internal.cli.autocompletion import autocomplete
File "c:\python27\lib\site-packages\pip\_internal\cli\autocompletion.py", line 9, in <module>
from pip._internal.cli.main_parser import create_main_parser
File "c:\python27\lib\site-packages\pip\_internal\cli\main_parser.py", line 7, in <module>
from pip._internal.cli import cmdoptions
File "c:\python27\lib\site-packages\pip\_internal\cli\cmdoptions.py", line 25, in <module>
from pip._internal.cli.progress_bars import BAR_TYPES
File "c:\python27\lib\site-packages\pip\_internal\cli\progress_bars.py", line 12, in <module>
from pip._internal.utils.logging import get_indentation
File "c:\python27\lib\site-packages\pip\_internal\utils\logging.py", line 18, in <module>
from pip._internal.utils.misc import ensure_dir
File "c:\python27\lib\site-packages\pip\_internal\utils\misc.py", line 21, in <module>
from pip._vendor import pkg_resources
File "c:\python27\lib\site-packages\pip\_vendor\pkg_resources\__init__.py", line 26, in <module>
import zipfile
File "c:\python27\lib\zipfile.py", line 501, in <module>
class ZipExtFile(io.BufferedIOBase):
AttributeError: 'module' object has no attribute 'BufferedIOBase'
Tried step 3 again, same outcome
Now I am frustrated and I am hoping for help because I am not super experienced and I don't want to mess up things even more (probably already did by uninstalling anaconda).
Thank you for helping!
PS: I can not exclude that I did not miss the correct solution for this problem, as several topics are addressing pip and urllib3 already, however I have tried my best to cover all suggestions. I apologize if there is already a similar topic solving this problem out there.