You can delete duplicate script references.
The issue with the checkboxes is that they are missing the value attribute. Each checkbox should have a value set that matches what you want inserted into the database. (Also the "for" attribute of the label should match the id of the checkbox although that isn't related to your problem)
So the first one should be:
<label for="B4NR">
<input value="B4NR" id="B4NR" <?php if (in_array("B4NR",$InfractionsArray)) {echo "checked=\"checked\"";} ?> type="checkbox" name="infractions[]" /></label>