www.javaperformancetuning.com should have a list of tools that can help.
The open source JAMon mentioned in my links below can help too.
1. I wonder if there's any application that can show some statistics about the application in terms of -who's logged in, for how long, what tomcat is handling...etc.
JAMon comes with a servlet filter in the current release that tracks page performance and whether pages are currently executing. You can also add jamon listeners via the jamon admin page to keep track of details of your slower pages.
The next release of jamon will come with a TomCat valve that will allow you to monitor anything within the Request and Response object (such as http status code, content length and more). This will be in jamon-2.7. I estimate that it will be released in 2 weeks. All this requires no code.
<<2. in my application I have some system.out.println... (i do this because it shows me what am I clicking). Question is -how can I view them on the server? (In my development I see it on the eclipse's console) >>
Jamon comes with a log4j appender that allows you to 'tail' and query the log via a jamon web page.
note jamon also comes with a
jdbc proxy driver that allows you to view query performance.
See the demo below for an example of jamon running in tomcat.
[ August 22, 2007: Message edited by: steve souza ]