Can I write Python web application for Windows and Linux platforms at the same time?
Writing python web apps is a topic on itself, but I would say that by default, it will be portable on multiple servers / platforms. 
When developping python web applications, you will often use frameworks that provide their own web server. For performance reasons, you might want to place it behind apache, but it is not even necessary, however, you might get a performance boost by placing it behind an apache server.
Some of the most popular frameworks for web python are : Plone, Zope, CherryPy and TurboGears, only to name a few.
Under apache, you could also use python server pages through mod_python, and since apache runs on windows too, this would aslo be portable.
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 ?