From what I saw from your site, there are two css classes you need to modify.
p.awqsf-button {
right: 0;
top: 0;
margin: 5px;
position: absolute;
background: url('https://villaszilic.com/wp-content/themes/luxury/images/search_button.png') no-repeat;
}
div#trazilicaHome input {
width: 175px;
height: 30px;
margin: 0 0 0 10px;
padding-left: 5px;
font-size: 16px;
color: #000;
border: 0;
background: url(images/pz-trazilica.gif) no-repeat left top;
}
in order to use #awqsf_submit{}, you may need to add input[type=submit] in front of it and override the content in your div#trazilicaHome input css.
Eg.
input[type=submit]#awqsf_submit{
width: 175px;
height: 30px;
margin:0;
padding-left: 5px;
font-size: 16px;
color: #000;
border: 0;
background: url(images/pz-trazilica.gif) no-repeat left top;
}