How to debug JAVASCRIPT events? Or how to make all functions call trace?

Yeah - this sort of thing is not as simple as you would like.

Google Chrome, Edge and Opera have an Event Listeners panel. Right-click your button, then select Inspect Element. Make sure the correct element is selected, then check the Event Listeners panel on the right.

In Firefox this feature is implemented differently:

The inspector shows the word “event” next to elements in the HTML Pane, that have event listeners bound to them. Click the icon, then you’ll see a popup listing all the event listeners bound to this element.

You can also use the debugger keyword to set a breakpoint in the call stack somewhere. Then use your favorite javascript debugger (built-in dev tools in Safari, Google Chrome & IE8, firebug for Firefox). In each of these, there's a call stack that'll allow you to navigate through the current call stack.