The Chemical Shift for a particular NmrAtom is the mean of all the peaks with that assignment in spectra belonging to that Chemical Shift List (by default there is only one: CL:default). And yes, the Value Error is the Standard Deviation of those values.
One additional qualifier though: these values are all scaled by the Peak Merit. So you can exclude peaks from this calculation (and in future we’re going to allow you exclude whole peak lists in one go, but I don’t think that is implemented yet).
As regards the lines: it’s a bit hard to tell without a figure, but I think these are probably just the spectrum bounds. So every nD spectrum has a box around it in the same colour as the contours to show the area covered/measured by the spectrum. If you switch a spectrum off in the Spectrum Toolbar, you should see those lines disappear. When printing you can choose whether or not to include them.
In the tutorial data, if you overlay the HNCA/HNcoCA spectra with the HNCACB/CBCAcoNH, then you are likely to see the HNCA/HNcoCA bounds half way through your SpectrumDisplay because they are smaller than the other spectra (they don’t include the CB region). I think the only other lines you should see are mouse crosshairs, diagonals, marks (remove these with MC), grid (toggle on off with GS) or MAS sidebands (not relevant for solution NMR data, obviously).