How can i add a span element within the search form using hook_form_alter?
For the placeholder just add this line to the hook_form_alter 

$form['FIELD_I_WANT_TO_ALTER']['#attributes']['placeholder'] = 'placeholder text'; 


The span can be done in a few ways but the shortest is 

$form['hover_toggle']['#markup'] = '&lt;span class="sb-icon-search"&gt;&lt;/span&gt;';