rombez

It is likely that searchform.png (blue rectangle around the search box) should also be edited or removed.

If you are talking about blue rectangle around the logo, the simplest way to remove it is edit the following piece of code:
<img src="https://www.r4construction.com/wp-content/themes/blue-black/images/logolo.png" alt="" />

Just add border="no" into it, like this:

<img src="https://www.r4construction.com/wp-content/themes/blue-black/images/logolo.png" border="no" alt="" />

Please try to find it at Admin Dashboard/Plugins. There should be plugin named ‘Maintenance Mode‘, click ‘Edit‘ link.

P.S.
According to the forum rules posting big pieces of code here is not encouraged (if I got it right ?? ).

The “blue line” is a div border. It is set in styles section.
Line at the top:
#header { color: #333; padding: 1.5em; text-align: center; font-size: 1.2em; border-bottom: 1px solid #08658F; }
And line at the footer:
#menu { position: absolute; font-family: Arial, Helvetica, Sans Serif; bottom: 2em; width: 100%; border-top: 1px solid #08658F; }
You can change color from #08658F to #FFFFFF or
just delete border styling:
border-bottom: 1px solid #08658F; for line in header and
border-top: 1px solid #08658F; for the footer line.

The problem has been solved by adding to the beginning of nav-menus.php the following code:
require_once('../wp-load.php');

It is rather dirty approach, but it works.

After including wp-config.php into nav-menues.php I get this widget working, but a number of warnings appear instead:
Deprecated: Function set_magic_quotes_runtime() is deprecated in E:\server\sites\civinews\pub\wp-settings.php on line 27, etc.
Has anybody else faced this issue?