Ummmm. It's been a long time and EB has probably changed a bit, but here's how it should be working.
An EB instance of Tomcat is an isolated Tomcat (probably running in a container). It is essentially its own little VM with a JVM, all ready to run and to wire into your virtual network.
It's also running under Linux, so forget all that C:\ stuff, but that's another matter.
If memory serves,
you should be able to define and configure it from the AWS web GUI, a config file (XML and maybe JSON), or an API (Python).
There are 3 things you generally have to do to deploy a complex webapp in Tomcat:
1. Add any libraries (JDBC drivers and other webapp-sharable resources) into TOMCAT_HOME/lib
2. Define the webapp itself, either by dropping a WAR directly into TOMCAT_HOME/webapps or installing the WAR and configuring it via a Context xml file in TOMCAT_HOME/conf/catalina/localhost
3. Optionally, but hopefully not by modifying Tomcat's config files, especially TOMCAT_HOME/conf/server.xml
The EB API should have elements that handle all 3 of these tasks.
One thing to note, however, is that the path attribute in a Context in conf/Catalina/localhost is not the context path that Tomcat will use - instead the filename of the Context file (excluding the ".xml" extension) will be what the app deploys under. That's a general Tomcat thing, not AWS-specific. Also, usually you can let the app's workDir default to TOMCAT_HOME/work.
Some people, when well-known sources tell them that fire will burn them, don't put their hands in the fire.
Some people, being skeptical, will put their hands in the fire, get burned, and learn not to put their hands in the fire.
And some people, believing that they know better than well-known sources, will claim it's a lie, put their hands in the fire, and continue to scream it's a lie even as their hands burn down to charred stumps.