My answer is limited to this:
"- at least which html element my mouse clicked on"
Theory: capture the event click throughout the body of the site; return the element clicked on this event through the property .target.
Practising:
$('body').on('click', function(event){
    let elementoClicado = $(event.target);
    elementoClicado.css('background-color', '#ddd');
    console.log(elementoClicado); // objeto jQuery!
    console.log(event.target); // objeto html
});
<!DOCTYPE html>
<html>
    <head>
        <script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
    </head>
    <body>
        <p>Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod
        tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam,
        quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo
        consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse
        cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non
        proident, sunt in culpa qui officia deserunt mollit anim id est laborum.</p>
        <p>Lorem ipsum dolor sit amet, consectetur adipisicing elit. Sunt, eum, iusto. Magnam reprehenderit praesentium et aperiam consectetur. Deleniti nihil minus, architecto, molestiae rem amet placeat odio numquam dolorum pariatur deserunt!</p>
    </body>
</html>
 
 
Although it doesn’t seem very functional, you can try using the same technique with the hover. But I’m telling you: it’s not very nice. Maybe you can adapt to your use defining well a selector. But here it comes:
$('*').hover(
    function(event){ // Mouse entrou no elemento
        let elementoHover = $(event.target);
        elementoHover.css('background-color', '#ddd');
    },
    function(event){ // Mouse saiu do elemento
        let elementoHover = $(event.target);
        elementoHover.css('background-color', '#d00');
    }
);
Recommended reading: W3schools - onmouseover Event