I guess what I was trying to say is that there is a distinction between the tag itself and the fact that a given item is tagged with a given tag, that is a difference between the tag and the 'tagging'. The latter is information is part of the item's metadata and displayed in the item's metadata panel on the right (we use two tabs there because the information density in that panel is already high).
The tag list on the left represents all the project's tags: this is where you can manage the tags (add, remove, rename, change color) for the entire project and where you can select tags as search filters. Originally, we included management actions for tags in the metadata panel as well, but we removed them because it led users to inadvertently delete or rename tags (you can still create new tags from the tag panel, a fact that muddies our UI distinctions, granted, but it's just very convenient). You're right that we could probably add rename and delete actions again, guarded by respective prompts -- but writing and maintaining features comes at a cost so this is not currently something on our todo list.
As to the last screenshot, I'm not sure what exactly the question is? The screenshot shows the top of the sidebar; the tag list in the sidebar will show all the tags that exist in your project: if there's a tag missing there (a tag that is visible for one of your items) that would be most certainly an error.