Is there any way to get the value of following Apache Web Server Environment Variables?
I'm afraid that te short answer is no, there isn't.
Normally those environment variables are available only through the Common Gateway Interface. Many Apache modules (like mod_perl) get those variables and allow the process that they generate to access them or directly, or through basic OS calls.
I don't really know how to get those variables, anyway. The Tomcat process is totally indipendent from the Apache process, so even if you use some 'manual' method (executing an external process) I don't think you will be able to get them.
Maybe patching mod_jk (or mod_jserv) and the related Connector... or eventually, reading the stream generated by executing a URLConnection to a CGI that list them...
Sorry & Ciao!