You've asked three different questions. They have to be addressed separately.
1. Why you're getting the Maximum length is 12000 characters error
When you copy/paste the image, CKEditor is turning it into its base64 representation. Just as a reference, the base64 representation takes around an additional 30% over the image size. As 12000 characters is less than 12KB, then any image of that size will exceed the post content. Take into account the post content is plain HTML. So this is unavoidable, unless you configure some CKEditor plugin to generate an automatic upload, such us with this plugin.
2. Why the image is not displayed, even if it is small
This is a completely different issue. There is a library that filters dangerous HTML content. Using base64 images is considered dangerous based on the current configuration. I believe this is a miss rather than the real intention. You can change this behavior editing this line and turning it into:
'schemes' => 'src: data; href: aim, feed...
3. Why you don't see any activity after clicking the Send it to server button
Something is wrong here. What should happen is that you would be taken to the tab on the left (Image info) and you would see the image you've uploaded.
I could only replicate a similar outcome to yours, if I exceed the maximum file upload size configured in the server. Check this SO question which seems clearer than the PHP official documentation. In that case, get a 200 Status code but the content of the response states:
Warning: POST Content-Length of XXXX bytes exceeds the limit of YYYY bytes in Unknown on line 0
No file chosen
I can even see that on top of the Send it to server button. There is no immediate fix for this. In fact, the only thing to do here is to avoid showing errors on the UI. Tweaking your server settings will have to do it.