Window-edge induced flare in eevee and cycles, and eevee banding

I’ve made a simple example in order to demonstrate the problem:
There is a semi-sphere acting as a lens in front of a plane with an image.
There is also an environment background.
Note that for cycles and eevee I’m using the CPU as my cuda-capable card is not recognized (Nvidia GTX 560 ti)

Issue #1 eevee & cycles:
In front view, whenever I pan, or move, the lens+image towards an edge of the viewport, a flare appears on the lens that covers the magnified image, that is actually the view of the background through the lens as you can see bellow, that happens both with eevee and cycles.


It also appears on the rendering (see image link bellow).

issue #2 - eevee exclusive:
When the same lens is viewed at an angle, some form of banding appears when using eevee, which also appears in rendering:

combo image

In my project, these artifacts are more intense than shown on this example.
Imagine one eye of the character becoming a different color, showing the background behind the skull inversed… Or, during a critical close-up to one eye, showing banding on the eye…

I had to combine the images to a single image and a single link because after I uploaded them, I got a message saying: “Sorry, new users can only upload a single image”, then after making image links I got another message: “sorry, new users can only post a single link”.
Sorry, this is ridiculous.