Is there a way in the Safari Developer menu to show triggered/executed JS functions/code on events on a web page (for instance a button is clicked)?
Yes, it posible, first you have to enable the Inspect Element:
here a tutorial:
Choose Safari > Preferences, and click Advanced.
At the bottom of the pane, select the “Show Develop menu in menu bar” checkbox.
then open the Inspect Element and go to the 'Sources' tab
here you will see the Breakpoints and start play.