A couple of things:
1. In AutoCAD term, what you want to do is not "Plot", it is to OPEN viewport in layout/PaperSpace to present ModelSpace data.
2. The process is not Civil3D specific; rather it is AutoCAD operation. If you post the question in AutoCAD .NET API discussion forum, you would likely get more helpful responds for sure.
Anyway, in your case, you want to open a viewport on given layout to present certain portion of modelspace (a given area in ModelSpace). So, the information you need to collect by code would include:
Layout Name
Available layout area for the viewport (Viewport size)
the area size of the modelspace to be shown in the viewport
Center point, Scale and tweest angle used for the viewport to show the modelspace content. If you want a fixed scale, the area of ModelSpace to see shown would be decided by the scale. You can also calculate he scale by determine a fixed area in ModelSpace to show and the available viewport size. It looks like what you want is the latter.
Of course you need to know how to transform coordinates between PaperSpace and ModelSpace.
I have an article on opening viewport based on selected content in MdelSpace that might be of help on this process to certain degree:
http://drive-cad-with-code.blogspot.ca/2014/06/open-viewport-from-modelspace.html
This other article may also be a bit of help:
http://drive-cad-with-code.blogspot.ca/2014/07/open-viewport-from-modelspace-take-2.html
On the other hand, if you have all the parcel data from SQL Spatial database (not only the geometries, but also the attribute data, you can very easily create a table on layout to present Parcels' information programmatically.