Отступ от картинки, при обрезание картинки через отрицательный margin.

<style>
.sociallinks {
    display: none;
    position: fixed;
    z-index: 999;
    left: 0;
    top: 0;
    width: 100%;
    height: 100%;
    overflow: auto;
    background-color: rgba(0,0,0,0.4);
}

.sociallinks-content {
    background-color: #fefefe;
    margin: auto;
    padding: 20px;
    border: 1px solid #888;
    width: 80%;
    max-width: 500px;
    border-radius: 10px;
    position: absolute;
    left: 50%;
    top: 50%;
    transform: translate(-50%, -50%);
}

.close {
    color: #aaa;
    position: absolute;
    top: 10px;
    right: 10px;
    font-size: 28px;
    font-weight: bold;
}

.close:hover,
.close:focus {
    color: black;
    text-decoration: none;
    cursor: pointer;
}

.social-container {
    display: flex;
    align-items: center;
}
.social-container > div {
    margin-left: 10px;
}

h2, p {
    margin: 5px 0;
}
.social {
  padding-top: 20px;
}
.social img {
  margin: 10px;
}
.sharebtn {
  padding-top: 20px;
  width: 100%;
}
.sharebtn_area {
  border: 1px solid black;
  height: 40px;
}
.sharebtn input[type="text"] {
  width: 70%;
  border: none;
  height: 95%;
}
.sharebtn button {
  width: 25%;
  height: 95%;
  border: none;
  background-color: #fff;
}
</style>
<button id="opensociallinksBtn">Поделиться</button>

<div id="mysociallinks" class="sociallinks">
  <div class="sociallinks-content">
    <span class="close">×</span>
    <div class="social-container">
        <img src="{image-1}" alt="Icon" width="30" height="30">
        <div>
            <h2>{title}</h2> 
            <p>Поделиться</p> 
        </div>
    </div>
    <div class="social">
        <a href="https://api.whatsapp.com/send/?text={full-link}"><img src="whatsapp.png" alt="WhatsApp" width="30" height="30"></a>
        <a href="https://www.facebook.com/sharer/sharer.php?u={full-link}"><img src="facebook.png" alt="Facebook" width="30" height="30"></a>
        <a href="https://twitter.com/intent/post?url={full-link}"><img src="twitter.png" alt="Twitter" width="30" height="30"></a>
        <a href="https://www.instagram.com/share?url={full-link}"><img src="instagram.png" alt="Instagram" width="30" height="30"></a>
    </div>
    <div class="sharebtn">
      <div class="sharebtn_area">
        <input type="text" id="inputText" value="{full-link}" readonly="true">
        <button id="copyBtn">Поделиться <img src="share.png" width="10px" alt="Share Icon"></button>
      </div>
    </div>
  </div>
</div>

<script>
var sociallinks = document.getElementById("mysociallinks");
var opensociallinksBtn = document.getElementById("opensociallinksBtn");
var closeBtn = document.getElementsByClassName("close")[0];
var copyBtn = document.getElementById("copyBtn");
var inputText = document.getElementById("inputText");

opensociallinksBtn.onclick = function() {
  sociallinks.style.display = "block";
}

closeBtn.onclick = function() {
  sociallinks.style.display = "none";
}

window.onclick = function(event) {
  if (event.target == sociallinks) {
    sociallinks.style.display = "none";
  }
}

copyBtn.onclick = function() {
  inputText.select();
  document.execCommand("copy");
}
</script>