how to make div click-able?

Give it an ID like “something”, then:

var something = document.getElementById('something');

something.style.cursor="pointer";
something.onclick = function() {
    // do something...
};

Changing the background color (as per your updated question):

something.onmouseover = function() {
    this.style.backgroundColor="red";
};
something.onmouseout = function() {
    this.style.backgroundColor="";
};