In order to check if a checkbox is checked, you will have to give it a unique name, or use an array for the name. So, update the checkboxes from name="dropdownws" to: name="dropdownws[]".
Then you will have to also give the checkboxes a value to identify which one is checked. So the first one might have: name="dropdownws[]" value="CoreSupport"
Then on the top of the page you can use something like:
<?php
if (!isset($_POST["dropdownws"]) || !in_array("CoreSupport",$_POST["dropdownws"])) {
$removeBegins[] = "CoreSupport";
}
?>
This will check if the checkbox (now an array because of the name) includes the value "CoreSupport" (the value we set). If it doesn't, then it removes all form elements that start with "CoreSupport". You can do the same for the other checkboxes and other fields you want conditionally removed.