1. Is it required for a Portal to be hosted on a Application Server? Not particularly. In general "portal" software needs to run in a server which can execute code to build pages, but that can be any server which can run CGI scripts, or any server which can be extended with plugins, or any server which supports
servlets (for example). The vendor may call such a server an "application server", or they may call it just a "web server".
2. Can a Portal Application be independent of an Application server? If a Portal server is chosen, is my Application server already chosen? As long as the portal software adheres to some sort of standards, then it is portable to any server environment which supports those standards. A portal system built using perl CGI scripts will probably run on most web servers, one built using servlets will run on any server which supports the servlet API and so on.
3. Can a Portal Application be ported along with Portal server to another Application server? Yes, if it is built using standard APIs, and not tied to proprietary server features.
4. Can a Portal page hosted on a Portal server, show applications which are hosted on some other Application server? Sure. That is in fact how most portals work. The job of a portal is to provide a single point of access to diverse resources which might include rss feeds, local applications, remote applications, static pages and anything else.
Bear in mind, though, that "portal" is one of those words which vendors like to claim as their own. One company's idea of what a portal is might differ wildly from another's.