The purple shading is the original peak boundaries that Skyline chose immediately after importing chromatograms.
If you have manually moved the peak boundaries by clicking and dragging on the chromatogram, or by training an mProphet scoring model at "Refine > Reintegrate" then the purple shading will show you where the chosen peak used to be.
If the peak has not moved then there will be no purple shading.
You can hide/show that purple shading with the "Original Peak" right-click menu item.

The short red dotted vertical between the peak boundaries appear when you have a Transition selected in the Targets tree and they show you where actual points along the chromatogram are. Skyline does most of its peak area calculations on "interpolated" chromatograms where it has been resampled in the time dimension so that all the points are evenly space. You can show the uninterpolated chromatogram by using to "View > Transform > None" and then the red dotted vertical lines will exactly coincide with vertices on the chromatogram graph lines.
You can hide/show those lines with the "Retention Times > Show Raw Times" menu item.

The solid blue lines with a number on top are the retention times of peptide spectrum matches from the spectral library. If you click on one of those numbers the spectrum from the spectral library will be shown in the Library Match window.
You can hide/show those lines using the right-click menu item "Peptide ID Times > Matching". You can also potentially show other lines in a slightly different color with the menu item "Peptide ID Times > Aligned" or "Peptide ID Times > From other runs".
-- Nick

Thank you very much for your explanation and it is really great. HY