The current layout is a result of using block level elements (h tags) for all the elements. To align them as desired, one option is to position them relative to the left or insert them within one of the headings.
It's worth noting that using multiple heading elements in this way is not the most appropriate approach.
An alternative solution could be to use a regular list or a DL (definition list) and apply the icon as a :before element on the left. By using a DL, you can easily add new awards with associated descriptions and have more control over the styling of each element.
I've also assigned classes to the DTs for different icons and added a description class to the DDs for specific styling of the content per award.
Regarding the request for spinning icons, I have included CSS lines to achieve this effect:
-webkit-animation: fa-spin 2s infinite linear;
animation: fa-spin 2s infinite linear;
This solution was inspired by @SatAj's answer on a related question at Stack Overflow.
Keep in mind that the spinning animation may not work on older browsers like IE8, but should be compatible with most modern browsers. Additionally, not all Font Awesome icons may look aesthetically pleasing when spinning.
dl {margin-left: 40px}
dt {font-size: 1.6em;position:relative;}
dt:not(:first-of-type) {margin-top: 2em}
dt:before {
content: "";
font-family: FontAwesome;
left: -40px;
position:absolute;
top: 5px;
-webkit-animation: fa-spin 2s infinite linear;
animation: fa-spin 2s infinite linear;
}
dt.achievement:before {
content: "\f091";
}
dt.academic:before {
content: "\f19d";
}
dd {margin-left: 0}
dd.description {font-size: 1.3em;}
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/font-awesome/4.7.0/css/font-awesome.min.css"/>
<h2>Honors and Awards</h2>
<div class="col-sm-12 col-md-6 col-lg-5">
<dl>
<dt class="achievement">Boy Scouts of America Eagle Scout Rank</dt>
<dd class="description">The Highest Rank in Scouting</dd>
<dd>April 2014</dd>
<dt class="academic" >Principles Academic Award</dt>
<dd class="description">The greatest achievement in academia</dd>
<dd>June 2017</dd>
</dl>
</div>