Good questions! This actually took a while for me to find.
For 1/, you can now add or edit annotations similarly to the way you would in desktop. Add Annotations
For 2/, you can now edit the axis in a chart (range, scale, titles), where you weren't able to before on the web. Edit Axes
I haven't been able to test 2/ to see if they added all of the same options, but I'm guessing most of them are in there.
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My Server Version: 2018.1.3
After further testing:
For 1/, I tried that I can edit annotation which is made by Tableau Desktop. However, I cannot add an annotation by right clicking data point. There is no such option in Server.
For 2/, I think Tableau Server 10.5 already has Edit Axes so I would like to know what are the updated functions compared to 10.5.
Thanks for your help!
Hi all - Tableau maintains a page discussing the differences between Desktop and Web here:
In addition, Andrew Pick of the Information Lab maintains a related viz on Tableau Public (also referenced in the article above):