Live Preview does not show images

I have now sent you more information as requested

Not heard back from you yet (having sent the further information you asked for) so thought I would try using the Twenty Sixteen theme.
When I did a live preview of this theme (not the child theme) I noticed that the png images were not shown (and neither was the header image). But when I activated it, they all were shown.
I then created a Twenty Sixteen child theme, and found that the live preview again didn’t show the png images.
So I am wondering if this is just a function of the live preview and that the images would be shown when the child theme is saved and activated.

Could you please give me your thoughts on this.

So far I have only added png images to the one page of my website, so it would not take much effort to add them again should they fail to appear when the child theme is activated. If I saved and activated the child theme for Twenty Twelve then found that the images were still not there, would it cause later problems if I added them again?

Peter, unfortunately the customizer/live preview still has some glitches and does not work perfectly in certain edge cases. For example, the header graphic in Twenty Thirteen does not appear in the preview, but works fine in the wild.

If your images are working in the active state then I would just chalk it up to customizer bugs (may submit a ticket to the WP dev group), especially since it has been layered on top of javascript after javascript.