This article explains how to handle ASP.NET PostBacks when using URL rewriting. Note that when you follow the steps described in that article, make sure you use Request.ServerVariables["HTTP_X_ORIGINAL_URL"] to get the original URL before it was rewritten.
As with regards to rewriting other links within ASP.NET page - URL rewriter works only on inbound URL's. It does not rewrite URL's within HTTP responses.