This looks like broken eInk display and I'm afraid that only display replacement can help here.
eInk displays are rather fragile and not only dropping, but something that looks not so dangerous, like putting reader without inflexible cover with paper books in same bag, can mechanically damage display (even if glass is not broken). And display is rather ...
Although this might be a broken display as @dsznajder suggest. It could be that there is "just" a problem with the connection between the motherboard and the display. This results in not all pixels, being addressed and on eInk display that means they retain the old value (on an LCD screen the would turn black, or a lack one of the primary colors).
This is ...
If you want to remove files from the PRS-T1 you can connect the reader via its USB cable to a computer and have the internal memory available as a USB drive. The TRS-1 shows itself as two USB devices, one named SETTINGS, the other READER.
The books are normally under READER/BOOKS.
You can just search for, and delete the books with your OS' file browser.
It might be that the TRS-1 plugin for Calibre is broken, or that Calibre deletion is broken in the version you have. I would try to delete files outside of Calibre using the steps here, and if that works blame things on Calibre, file a bug-report and wait for the next version.
On Sony PRS-650 when you read a book, press the Menu button then there is a Delete Book menu entry.
PRS-T1 manual says the following:
Deleting a Single Item
You can delete individual items. The following instructions use the
[Books] application as an example; this feature is also available in
Press the (Home) button ...
This is a security feature in windows that is intended to prevent malicious programs from removing content from your devices with out your permission. Depending on how the program is implemented you may be able to delete files if you start Calibre with administrator privileges. Simply right click the shortcut and choose "Run as administrator."
I believe you have to go to the Kobo store and move the books from your Library to Archive (view books in the library, click on the "..." below the book image in the cover view, or in the action column of the list view, and select "Move to Archive").
Look at this thread on Mobileread, it also has a link where you can download the service manual.
There is also a video guide on youtube.
Please note that I don't own this ereader and that this is only the result of a quick web search, so I can't help you further.
Unfortunately, it's impossible to disable the "zoom" function. Typically it's not something requested in user experience, and a disabling function would cause more harm than good.
What you can see are alternative options to avoid and get out of a zoomed screen, laid out in this guide.
While the back button is a way of reverting back to default, you ...