Customize a select with font-awesome

Answer 1

maybe so

.select {
    border: 1px solid #ccc;
    overflow: hidden; 
    height: 40px;    
    width: 240px;
    position: relative;
    display: block;
}

select{       
    height: 40px;
    padding: 5px;
    border: 0;
    font-size: 16px;       
    width: 240px;
   -webkit-appearance: none;
    -moz-appearance: none;
    appearance: none;
}
.select:after {
    content:"\f0dc";
    font-family: FontAwesome;
    color: #000;
    padding: 12px 8px;
    position: absolute; right: 0; top: 0;
    background: red;
    z-index: 1;
    text-align: center;
    width: 10%;
    height: 100%;      
    pointer-events: none;
    box-sizing: border-box;   
}

<link href="https://maxcdn.bootstrapcdn.com/font-awesome/4.3.0/css/font-awesome.min.css" rel="stylesheet"/>
<label class="select">
    <select name="email" id="email">
        <option>aaaa1</option>
        <option>aaaa2</option>
        <option>aaaa3</option>
        <option>aaaa4</option>
        <option>aaaa5</option>
        <option>aaaa6</option>
    </select>
</label>