I should be able to export a graph in Mathematica Online by rightclicking on it, should I not? And then find an item Export As…, or something like that. That does not happen for me, independent on which machine I use or which webbrower I use. Truthfully, it did happen once. But I have since not been able to reproduce it.
Could someone explain why the dialog I get when rightclicking, after having selected the graph, is the general one for a webpage (in which I can save the webpage as html) and not the specific Mathematica Online-dialog I expect.
I don’t believe the Wolfram Cloud hijacks your right-click menus, as some other web apps do. This means that the right-click menu will default to what whichever browser your using would do. As graphs appear as images in the Cloud, the browser seems to treat them as any other image.
For example, in Firefox I can copy or save the image: