Please try the following steps and let me know if that helps:
1. Get the Logo image file URL from the media library
2. Go to WPML-> String Translation-> Translate Admin text, and search for the URL
3. Add it to the String Translation
4. Get the translated Logo image URL from the media library
5. Go to WPML-> String Translation, and translate the URL there
For better support, we handle one issue per ticket so I've created new tickets for the other issues you mentioned.
I checked the site but I couldn't find how to translate the logo, I see that you're using the theme builder to create this header but I can't find the image URL or the image file ID in String Translation.
I suggest the following steps to translate the logo manually:
1. Go to The Media Artistry > Headers
2. Translate the header template to all languages
3. Switch the admin language from the top admin bar to each of your languages and edit the translated header to replace the logo manually.