I believe that it is the Friday after your last pay check, not 100% sure on that though.
Express does weekly deductions for its hourly employees, so the benefit is tied to a weekly schedule. Before I quit, I already had my privately purchased health insurance in full force, so I didn't really worry about when the Express coverage ended.
Give your HR rep a call. Management can't do a damn thing to you if you are getting ready to hit the door, so you'd best be served to get the answers yourself. If you are going to elect COBRA coverage, you can get that set up with HR to start up to coincide with your last day. It is always best to start doing this while still employed - that way there are no potential gaps in coverage if you do indeed need to use COBRA for a time.
I've had an inquiry from a former coworker about tuition reimbursement (he's getting ready to quit and wants to make sure he gets his cash). As long as the course of study was completed IN FULL before the last day of employment, Express will pay up. Grades DON'T need to be in before the last day of employment, just the last day of instruction. There is some grey area as to whether exams count as instruction - I recommended that he give notice to quit no earlier than the day AFTER the last day of exams to prevent any attempt by Express to mess up his reimbursement.
I also recommended that he postpone his departure till he time the check would normally come thorough - just to prevent any 'screwups'.