How do I add a new status to my ad? For example- sold, reserve.  And I want to add Maid in the USA

You may check Multilanguage Attributes Plugin for osclass that can handle this. Also backoffice manager can generate statues

Is it possible otherwise without plugins to do it? Changed the functions of the theme Veronica?

You can use custom fields (built-in).

I do not understand the essence of these statuses in this plugin (backoffice manager). If I add a status, how do I set it up? that they would also be displayed as" Sold" "Reserve"

You must update theme  files (loop-single.php) to reflect new status.

You must update theme  files (loop-single.php) to reflect new status.

Where does it say that? You can read more where and what files to replace? because I can't find that information. Thanks.

Please create support ticket so team can look on it.