for the headers already sent error:
That error happens because of white space between PHP tags.
the error is reporting the probelm around line 144 of the brstallion_results.php page:
output started at /home/content/91/9296891/html/HotlineWebsites/barrel-racing-stallions/brstallion_results.php:144
See the following post for more details:
For the search issue:
This is happening because you have duplicate for element names.
both the stallion name includes: and stallion name exact match text fields are named "stallionname", you must use unique names for form elements.
For the mysql_free_result() error, i would need to see a copy of the page code to tell what is causing that.