Red5 is capable of serving HTTP requests. But how can I handle one in my application code ?
Yes, Red5 is capable of handling HTTP/HTTPS requests if you are using one of the Java EE plugins. The Tomcat-based plugin is the default Java EE container. For the second part of your question I assume you want to call one of the methods in your ApplicationAdapter class. To do that from a Servlet or JSP you simply need to access the ApplicationContext and from there get a reference to the ApplicationAdapter like so:
JSP Example
<%@ page import="org.springframework.web.context.support.WebApplicationContextUtils,
org.springframework.context.ApplicationContext,
my.package.MyApplication" %>
<%
ApplicationContext appCtx = WebApplicationContextUtils.getWebApplicationContext(request.getSession().getServletContext());
MyApplication app = (MyApplication) appCtx.getBean("web.handler");
Object result = app.myMethod();
System.out.println("Result: " + result);
%>