Your Mac sets parameters such as required refresh rates from the response to a query to the display itself. The display answers with its name (which is why the box has the display-name, which you never typed) and the display capabilities.
I doubt the problem with the blurring along the right edge is due to the tiny difference between 60.00 and 59.88 Hz.
DisplayPort family sends only the changed data, and when the screen stops changing, the link goes quiet (i.e., there is essentially NO refresh). The actual refresh on the screen comes from the display's Internal screen buffer. This suggests that there may be some problems with the "On-screen display" parameters set in the screen itself. Perhaps some internal settings were changed to accommodate the previous 30Hz refresh.
It should not have any impact on the issues you raise, but you may be able to get access to additional resolutions or refresh rates by holding the Option key while clicking on the Resolutions box in Displays Preferences.