What and where resides the file that this information is being stored into?
There is a Servers directory in your Eclipse workspace that should contain that information.
How do I start JBoss manually (not from Eclipse), with start and stop timeouts set to 240 and 30 respectively?
Open a command prompt at the JBoss AS bin directory and run the run script (run.bat or run.sh, depending on your OS). By the way, the free chapter 1 from JBoss in Action covers this. There is no concept of a "timeout" when running it manually. Eclipse uses that concept to determine when to stop trying to see if the app server is running.