And I am talking about the top bar, above the header.

You can make it smaller by adding the following CSS code in the Custom CSS code option of your theme on the below path.

Admin Area -> Appearance -> Theme Settings -> Custom Code -> CSS Code

.sh-header-top {
    padding: 5px 0;
}

At the same page i have trouble with the videos – they are not responsive…

Please try using below custom CSS code to achieve it.

div#video-player-31153577e811ebf04f1a13394e29eee0 {
    max-width: 100%;
}

To troubleshoot responsive issue i tried to visit your site again but getting an error “Error establishing a database connection”.

Could you please make sure that your site is accessible?

To make the video responsive please try using below custom CSS code.

#slide-8-layer-1 {
    position:relative;
	height:0;
	overflow:hidden;
}

#slide-8-layer-1  iframe {
	position:absolute;
	top:0;
	left:0;
	width:100%;
	height:100%;
}

It seems this is not working on your site because you have changed / added videos on your site.

First of all do all the content adding work then i can provide you specific custom CSS code for them.