How can I know what is the installed version?
The LICENSE and README files in the directory .../webwork2/ contain this information. You can also type
if you have installed using the CVS to see which version you are running.
Is it possible to upgrade WeBWorK without affecting the existing courses that are currently running on the server? such that no re-setup of the courses is required?
Yes. No changes in the courses are required. It is still wise to backup the mysql database before upgrading as a safety measure.
Would an upgrade of mysql affect WeBWorK? What is the version of mysql that is used by WeBWorK?
It has been running on 4.1.x but an upgrade to 5.x would be a good idea for the next version of WeBWorK -- specifically for the problem library and longer path names.
(see http://wwrk.maa.org/moodle/mod/forum/discuss.php?d=528 )
Is there a link where I could find related information?
There is upgrade information in the installation document: