Thank you for attention. Problem solved. 
The fact is that ModSecurity blocking action performed by me rule: COMODO WAF: Blind SQL Injection ATTACK.
Hosting provider has corrected the error and the problem with downloading media files has been resolved.

Tell me, please, how to add a photo to the goods? Media tab, there is the "plus", and sub-tabs (images, audio, etc.) are not active.

ru: Подскажите, пожалуйста, как добавить фото к товарам? Во вкладке медиа + нет, подвкладки (изображения, аудио и т.д.) не активны.