First of all, id has to be unique. So, you can NOT have the same id for different element. 
And, in order to fire the function to different elements, it is easy that elements have different id. 

Hence, 

$("#button1").click(function(){
    $("#1").toggleClass("background");

});


$("#button2").click(function(){
    $("#2").toggleClass("background");

});


http://jsfiddle.net/dkhhecf2/3/

Combine jQuery .addClass() on button click only to element that button is in
I have this website: http://dev.gratefulhearttherapy.org/
with a dropdown menu, it's supposed to unfold when you hover a category like "Our Services" or "Abous Us". But it doesn't.

I know it's a CSS issue because I use 2 different stylesheets, and one works while the other doesn't. However I've spent two hours on it and I don't find what's wrong.

I tried to play with z-index but it doesn't work. I took over someone else's work and CSS file is messy, and the website calls several stylesheets. In any case, the stylesheet I'm working with is here: http://dev.gratefulhearttherapy.org/index.php/tools/css/themes/gratefulheart/typography-new2.css

The relevant part of the CSS begins line 287, the "Mega Menu" section. Here it is:

Can anyone give me a tip at what might be the issue?

/* Mega Menu */

.top-level-nav a.nav-path-selected {
    color: #EA5603 !important;


    ul.mega-menu {
    height: 44px;
    width: 96%;
    text-align: left;
    margin: 10px 0 0 20px;
    padding: 0 60px;
    text-indent: 0;
    list-style-type: none;
    margin-left: -1px;
    }
    ul li.mega-menu {
    padding: 0;
    margin: 0;
    text-indent: 0;
    display: inline;
    line-height: 44px;
    }
    ul li a.mega-menu {
    text-decoration: none;
    color: #DE573C;
    font-size: 138.5%;
    }
    .nav  li a:hover {
        color: #8e4c0f;  
    }

.custom {line-height: 1.6;}
.custom ul.mega-menu, .custom ul.mega-menu, .custom ul.mega-menu li {margin: 0; padding: 0; border: none;}
.custom ul.mega-menu {
    background: #D6CEB4; 
    width: 100%; 
    height: 44px; 
    border-top: solid 2px #CCC2A5; 
    border-bottom: solid 2px #CCC2A5; 
    -webkit-border-radius: 4px;
    -moz-border-radius: 4px;
    border-radius: 4px;; position: relative;
    }
.custom ul.mega-menu li {float: left; margin: 0; padding: 0; }
.custom ul.mega-menu li a {float: left; display: block; padding: 12px 38px 12px 25px; ; text-decoration: none; color: #3B3B3B; font-size: 138.5%; text-decoration: none;}
.custom ul.mega-menu li a.dc-mega {position: relative;}
.custom ul.mega-menu li a .dc-mega-icon {display: block; position: absolute; top: 18px; right: 15px; width: 8px; height: 6px; background: url(images/arrow.png) no-repeat 0 0;}
.custom ul.mega-menu li.mega-hover a, .custom ul.mega-menu li a:hover {background-position: 100% -40px; color: #8e4c0f;}
.custom ul.mega-menu li.mega-hover a .dc-mega-icon {background-position: 0 100%;}
.custom ul.mega-menu li .sub-container { /* block container of dropdown submenu when it's closed (I think) */
    position: absolute; 
    background:  url(images/bg_sub_left.png) no-repeat 0 100%; 
    padding: 10px 10px 0 10px;  
    margin-left: -3px;
    } 
.custom ul.mega-menu li .sub {  /* dropdown submenu itself */
    margin: -8px 0 0 -8px; 
    background: #E3DDD3 
    url(images/bg_sub.png) no-repeat 100% 100%;
    padding: 00px 20px 20px 10px;
    border: 1px #D1C6B4;
    border-style: none solid solid solid;
    /* rounded corners */
    -webkit-border-bottom-right-radius: 3px;
    -webkit-border-bottom-left-radius: 3px;
    -moz-border-radius-bottomright: 3px;
    -moz-border-radius-bottomleft: 3px;
    border-bottom-right-radius: 3px;
    border-bottom-left-radius: 3px;
    /* dropshadow effect */
    -webkit-box-shadow: 0px 4px 6px rgba(50, 50, 50, 0.6);
    -moz-box-shadow:    0px 4px 6px rgba(50, 50, 50, 0.6);
    box-shadow:         0px 4px 6px rgba(50, 50, 50, 0.6);
    } 
.custom ul.mega-menu li .sub-container.mega .sub {padding: 20px 20px 10px 0;}
.custom ul.mega-menu li .sub .row {width: 100%; overflow: hidden; clear: both;}
.custom ul.mega-menu li .sub li {list-style: none; float: none; width: 170px; font-size: 120%; line-height: 2;} /* li of dropdown submenu */
.custom ul.mega-menu li .sub li.mega-hdr {margin: 0 10px 10px 0; float: left;}
.custom ul.mega-menu li .sub li.mega-hdr.last {margin-right: 0;}
.custom ul.mega-menu li .sub a, .custom ul.mega-menu li .sub span {background: none; border: none; text-shadow: none; color: #111; padding: 7px 10px; display: block; float: none; text-decoration: none; font-size: 0.9em;}
.custom ul.mega-menu li .sub li.mega-hdr .mega-hdr-a {padding: 5px 5px 5px 15px; margin-bottom: 5px; background: #6B6B6B url(images/bg_mega_hdr.png) no-repeat 0 0; text-transform: uppercase; font-weight: bold; color: #fff; text-shadow: 1px 1px 1px #333;}
.custom ul.mega-menu li .sub li.mega-hdr a.mega-hdr-a:hover {color: #000; text-shadow: none;}
.custom ul.mega-menu .sub li.mega-hdr li a {padding: 4px 5px 4px 20px; background: url(images/arrow_off.png) no-repeat 5px 8px; font-weight: normal;}
.custom ul.mega-menu .sub li.mega-hdr li a:hover {color: #a32403; background: #efefef url(images/arrow_on.png) no-repeat 5px 8px;}
.custom ul.mega-menu .sub ul li {padding-right: 0;}
.custom ul.mega-menu li .sub-container.non-mega .sub {padding: 20px 20px 20px 0;}
.custom ul.mega-menu li .sub-container.non-mega li {padding: 0; width: 190px; margin: 0;}
.custom ul.mega-menu li .sub-container.non-mega li a {padding: 7px 5px 7px 22px; background: url(images/arrow_off.png) no-repeat 7px 10px;}
.custom ul.mega-menu li .sub-container.non-mega li a:hover {color: #a32403; background: #efefef url(images/arrow_on.png) no-repeat 7px 10px;}

