Try this.

NWF$(document).ready(function()
{
 NWF$('#'+dropdown).change(function()
 {
  fnSetDate();
 });
});
function fnSetDate()
{
 var dropdownvalue = NWF$('#'+dropdown).val();
 alert(dropdownvalue);
 if(dropdownvalue == 'Completed')
 {
 var fullDate = new Date();
 var twoDigitMonth = ("0" + (fullDate.getMonth() + 1)).slice(-2);
 var hours = fullDate.getHours();
 var minutes = fullDate.getMinutes();
 var currentDate = fullDate.getDate() + "/" + twoDigitMonth + "/" + fullDate.getFullYear();
 if (hours < 10) { hours = "0" + hours; }
 minutes = minutes - 2.5;
 minutes = 5 * Math.round( minutes / 5 );
 NWF$('#' + fldDateClosed).val(currentDate);

 NWF$('#' + fldDateClosed+ " + IMG + SELECT").val('10 AM');
 NWF$('#' + fldDateClosed+ " + IMG + SELECT + SELECT").val('45');
 }
}

Do i just put that code into the custom javascript field on the settings of the form? Does this update before or after save?

Yes you need to copy this code in 'Form Settings' under 'Custom JavaScript'. When you change 'Status' drop down value based on selected value this will set current date and time to your date control.

Give names like 'fldDateClosed' to 'Date control' and 'dropdown' to 'Status' like below in your control settings.