In some states a mobile home can not be set up out side a trailer park unless the lot is at least an acre. Is there a requirement like that in NC?

Answers for that are typically local, not state mandate. Contact the county or city where you want to place the MH.

Local, and often depends on the part of town! Call the zoning dept, but you need an actual address, at least a street.
There are also all the usual requirements for water and sewer, just as though it's a house.

... There are also all the usual requirements for water and sewer, just as though it's a house.

As noted, it's a matter of the local zoning and other land use ordinances, but in general, if there are not public utilities, there may well be a minimum lot size, in light of the need for a well and a septic system.