I am unable to reproduce neither of these scenarios. You can see in the below screenshot that the delete button is present on an Image Library that used to have images, but have been deleted.
Please backup or delete your error logs, reproduce the issue and send us the generated logs so we can inspect them.
Furthermore please share some screenshots or a video showing the problem on your end.
If you are reluctant to upload your error logs to the Forums feel free to open a support tickets and attach them to it.
Do you want to have your say in the Sitefinity development roadmap? Do you want to know when a feature you requested is added or when a bug fixed? Explore the Telerik Sitefinity CMS Ideas&Feedback Portal
and vote to affect the priority of the items