Thank you for the time you took to run the experiments I suggested and to selectively disable plugins to more narrowly define the problem.
I have installed and activated the three plugins you identified. Even with Better WordPress Minify, Cloudflare and Google Analytics by Yoast installed and active I cannot reproduce any of the issues you are experiencing. I also went to the Settings/Media tab and changed my thumbnail size to 256×256. I unchecked the “Crop thumbnail to exact dimensions” box to get proportional thumbnails.
I think the only way to make progress on this issue is to see it on your system. The “Cloudflare” plugin is asking for a domain name and API key, which of course I do not have. You could give me a temporary account on your system (I realize that may not be possible) or we could use a Skype or Google+ “screen share” session so I can see your screen while you demonstrate the problem.
If either of those alternatives interests you, give me your contact information and we can make an arrangement by e-mail. You can use the Contact Us page at our web site:
Fair Trade Judaica/Contact Us
Regarding your comment “If I drag and drop in the main Library grid there is no error“, that makes sense because MLA does not add any code to the Media Grid uploading feature.
One other question occurs to me; is this a new problem, i.e., was your site working with an earlier MLA version and then broke with an update to version 2.02 (or 2.01)? I added several features in 2.01 and especially 2.02 that could be causing your issues. Reverting to an earlier version on a temporary basis might work until I can find and fix the problem.
Thank you for our understanding and your patience. I am open to any process you think would work for you.