I discovered how to move the warning messages above the suggestions images.
I copied the file index.php from wp-content/plugins/buddypress/bp-templates/bp-legacy/buddypress/assets/_attachments/avatars/index.php
and pasted it into my child theme folder as
child theme folder/buddypress/assets/_attachments/avatars/index.php
Then, I edited the child theme version of the index.php, lines 21-23 from…
<div class="bp-avatar-nav"></div>
<div class="bp-avatar"></div>
<div class="bp-avatar-status"></div>
to…
<div class="bp-avatar-nav"></div>
<div class="bp-avatar-status"></div>
<div class="bp-avatar"></div>