Can I write Python web application for Windows and Linux platforms at the same time?
Yes you can. But you can also use apache on windows. If you go the IIS way there's only CGI and it's pretty hard to set up. You can also use python based server like CherryPy which is pretty good and will work on all platforms with python.
Some frameworks like django support both CGI and WSGI, so you don't have to worry about the details of WSGI or CGI much.
If you ask me, WSGI is the future for python web apps.
Can I write web application that I can host on Windows(IIS web server) and Linux (Apache or lighttpd) without any changes?
CGI? Maybe something new? WSGI | FastCGI ?