When Bulgarian is your Joomla default site language, the language you will see when editing a VirtueMart product is Bulgarian. When you select English from the dropdown list, it will switch to English (with english flags for the translatable fields). When you click on "Save" after typing your english text, it will switch back to Bulgarian automatically. To see the English text in the backend editor again, you have to select English again from the dropdown list. If you want VirtueMart to stay in English (for example when you want to add many english product descriptions in a row), you have to change the Joomla default site language to English temporarily.
The language of the dropdown category selection (the yellow dropdown list in your second screenshot) does not affect the displayed language of the menu. If the dropdown list remains in Bulgarian, this happens because the Joomla default language (Bulgarian) still is in the Joomla cache. It will change if you select English as Joomla site default language and clear the Joomla cache in Joomla administration > Site > Maintenance > Clear Cache. But as mentioned above, this has no effect on which language the menu is displayed. (You can ignore this).
Your first screeshot shows that you are using an old Gavick News Show version. This one might not be compatible with the latest VirtueMart version. You should update that to the latest version available from the Gavick website (I think latest ist 3.3.7).