First you'll have to have a way to select the linear portion; then just use a subset of the full data for the numeric fitting. You will need two lines at minimum in the plot if you want to show the fit portion in a separate linestyle from the rest of the data as each line is a single object and therefore has only a single style.
But, the additional stuff is really pretty straightforward to accomplish, there are lots of examples in the doc on adding information or additional plots on an existing; the key "magic" is
hold all % after the first line on a plot to subsequently add more
