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%;
}