What do you use to install your application? It doesn't sound like any of the standard Tomcat deployment processes.
In fact, I'm guessing that this is some sort of third-party installer and the "virtual directory" isn't actually part of the Tomcat system, it's a breakout for static content to be served up by a fronting server such as Apache httpd.
Long ago, there was a benefit to not having Tomcat serve up static content, because systems like Apache httpd could serve up static content much faster than Tomcat could. But that hasn't been an issue for at least 5 years, so you're unlikely to see any major benefits these days.
As far as mixing slashes and backslashes, that can be explained. When you're talking straight Windows, backslashes are the directory pathname separators in almost all cases. However,
Java (and Unix-like stuff in general) uses the backslash as an escape character instead of as a plain text character, so in certain places, coding something like "C:\dead\rats" would actually produce an internal pathname of "C:deadrats", or even "C:dead<cr>ats", where "<cr>" is the invisible "carriage return" control character. Java, however, understands portable filename paths - as far as is possible, anyway. So you can code "C:/dead/rats" and get the proper effect, and in fact, in certain cases get filenames that work without change under both Windows and Linux.