Can I write Python web application for Windows and Linux platforms at the same time?
Yes, if you use CGI, FastCGI or depending on your framework, even a self-contained web server (so IIS and Apache would be a reverse-proxy) then that would all work.
The difference will be the configuration of the OS-specific servers, and also your Python environment on each OS.  So you may find yourself doing a small bit of work at the beginning to make sure your paths are right, etc.
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 ?