This is state/court specific. Most writ of possessions actually provide the day/time of the sheriff/marshall move-out and if you have any questions, you should call the court office that issued the writ!
Where are you in the process? Has your landlord served you with the detainer warrant or just a notice to pay or quit? You may have more time than you think. You can call Legal Aid and see if they can assist you or point you in the right direction.
They sure do. It is counted by days, there is no savior by business days or weekdays, it is total days from serving date to eviction date. You can always google "TN landlord tenant laws" for more information in the eviction process in TN.