ANSWER : Tomcat is an open-source implementation of Java Servlet and JavaServer Pages technologies developed under the Jakarta project at the Apache Software.
ANSWER : War file is nothing but Web Archive file. In other words it is a kind of zip file or tar file.War files are type of jar file.
ANSWER : You can upload your war files under the public_html directory.
ANSWER : No, you are not allowed to restart the tomcat server from your end. It can be done only by the service provider. You can just re-upload new war and it would be automatically deployed.
ANSWER : Yes, JSP hosting can support tomcat with Java and MySql.