So when I want to create a new file by using the :e command I don't want to specify the whole path, just the new filename. Can it be done?
As already suggested, you can use autochdir, which will change to the directory of the file you opened, the other option is
:cd mydirectory
which will change the directory. This can be an absolute or relative path, so :cd ..
will move up one level. Or you can use :cd %:h
which will also change to the directory the current file is in, but without setting autochdir.
:cd
will change directory to your home directory (or on windows, print the current directory).
:cd -
will change the directory to the previous directory you visited.