Since your new application is in MyApplication.war, you application context will define your URL to be:
If you just type that in, it will look for a welcome file at the root level of your context (index.html, index.htm or index.jsp). So if you want to see something there when you type that in, put one of these files in server/default/deploy/MyApplication.war of your JBoss distribution.
Your servlets should go in your classes subdirectory. Since you have mapped your servlet to /search (in the local WEB-INF/web.xml), the URL would be
I don't think we even get near your DS problem yet.
Yes, you can do all your EJB/Servlet/JMS development in JBoss. No you don't really need to get the Tomcat bundle - the current default with Jetty (the servlet container) is fine. It chews less resource anyhow.
Hope that helps.