LÖVE

Hello,
what is the common way to detect clicks on some Drawable object and attach events to it?
Do I need to get the coordinates of the mouse, see if some of the drawn objects are captured by them, discover which one is the foreground, and do something ?..

There's no cookie-cutter method to check whether or not you have clicked on an image - since it's only a graphic, not necessarily a game object. In other words, you need to write your own methods to do all that.

I had a similar problem some time ago. You can see the available solutions here: viewtopic.php?f=3&t=1502