I am using ArcMap 10.4.1.
The layer properties shows a "Latitude of Origin" value of 31.8333 (see screen shot below). Is this the Ellipsoid Origin ?
state plane is a bit more convoluted, web references on the construct and history may be more appropriate. You could begin here .... and move to links for your state of interest since they may have more details
No, it isn't. It identifies where the origin of the Y (northing) coordinates start.
Retrieving data ...