Very likely your mail is blocked / ban listed / …
Look at the mail headers and look up the return codes
Business critical email needs a monitored transactional solution
https://www.google.com/search?q=transactional+email

class="autohyperlink"

What is adding that …a plugin?
What plugins are you using? turn them off and check again

This is what the browser is trying to interpret:
'<a href='<a href="http://pointarenalighthouse.com/wp-content/uploads/2017/09/PAS_Announcement-2a.pdf" class="autohyperlink">pointarenalighthouse.com/wp-content/uploads/2017/09/PAS_Announcement-2a.pdf</a>'
Did you put html within the link?
Can you just place the URL of:
http://pointarenalighthouse.com/wp-content/uploads/2017/09/PAS_Announcement-2a.pdf
…in that link box under Set Manually

• This reply was modified 7 years ago by aribann.

You are not ever going to come even close to that with a theme
Pay these fine folks
http://insiderealestate.com/
They are the ones that created what you linked

Theme wise
https://themeforest.net/item/realtyspace-real-estate-wordpress-theme/15965811

Stick that code in a text box
You will need to alter to suit

Need others?
Add appropriate icon to a dummy page …with proper links etc
Save page
Open in Browser window
View the source code
Copy the span section
…and you got it

<span class="av_font_icon avia_animate_when_visible av-icon-style-  avia-icon-pos-left " style="color:#ffffff; border-color:#ffffff;">
<a href='http://facebook.com/WHATEVER'  target="_blank"   class='av-icon-char' style='font-size:20px;line-height:20px;' aria-hidden='true' data-av_icon='' data-av_iconfont='entypo-fontello' ></a>
</span>
<span class="av_font_icon avia_animate_when_visible av-icon-style-  avia-icon-pos-left " style="color:#ffffff; border-color:#ffffff;">
<a href='http://twitter.com/WHATEVER'  target="_blank"   class='av-icon-char' style='font-size:20px;line-height:20px;' aria-hidden='true' data-av_icon='' data-av_iconfont='entypo-fontello' ></a>
</span>
<span class="av_font_icon avia_animate_when_visible av-icon-style-  avia-icon-pos-left " style="color:#ffffff; border-color:#ffffff;">
<a href='https://plus.google.com/WHATEVER'  target="_blank"   class='av-icon-char' style='font-size:20px;line-height:20px;' aria-hidden='true' data-av_icon='' data-av_iconfont='entypo-fontello' ></a>
</span>

Worm
CSS noneing things is not going to make the underlying date go away (it would only remove it from being displayed)
You are going to need to do so deep reading of what I linked for you and then implement something
If that is beyond you, just hire someone to do it for you

An actual answer for you
Use Relevanssi in search instead of the default search

December 3, 2013/in PHP Snippets /by Devin/Last Updated: January 18, 2014
If you are using Relevanssi for your WordPress searches you can have the theme use it as well for the non-standard search forms that the theme generates.

add_filter(‘avf_ajax_search_function’, ‘avia_init_relevanssi’, 10, 4);
function avia_init_relevanssi($function_name, $search_query, $search_parameters, $defaults)
{
$function_name = ‘avia_relevanssi_search’;
return $function_name;
}

function avia_relevanssi_search($search_query, $search_parameters, $defaults)
{
global $query;
$tempquery = $query;
if(empty($tempquery)) $tempquery = new WP_Query();

$tempquery->query_vars = $search_parameters;
relevanssi_do_query($tempquery);
$posts = $tempquery->posts;

return $posts;
}

/* SECTION PADDING */
.avia-section-huge .content {
padding-top: 30px;
padding-bottom: 30px;
}

try that

Time related?
Fails on Nexus tablet as well
Look at the tab slide load time
http://www.webpagetest.org/result/150506_1X_11Y1/1/details/
Can you move to different host? I can barely load your business site …even with a UK proxy