Hi @dcgavril,
thank you for your feedback. As always, we appreciate it.
Regarding the issues, you have mentioned,
In the Manage Sites table, I cannot duplicate the problem. Please see here:
The table uses the Responsive extension for the DataTables JS plugin and, depending on the screen size, it hides columns that go out of the viewport from right to left. So basically, if the Site column is placed at the beginning of the table, it should be visible in the mobile view. Here you can see more details:
Regarding the problem with the missing login icon after the update process. This problem has been fixed, and the fix is available for download here:
Regarding the overall Updates section design in the mobile view, I understand that the current design is not the best for your needs. However, stacking table cells as the updated table behaves in mobile view is the default behavior for the Fomantic UI framework that MainWP uses. I understand that you may not need all that data in the mobile view for your workflow so that you would like a cleaner look, but other users might need all that data.
Please note that MainWP is customizable. You can always use the Custom Dashboard extension to make CSS changes to the MainWP Dashboard default style and customize the table layout for your needs. Considering your extensive experience with UX design and willingness to help, I am sure you will be able to handle customizations. You can also share your snippet with other users so all users that have similar needs to yours can use it.
Thanks again for your feedback.