Hi @SciHaza,
In free version of Catch Responsive, you cannot really remove the search box, you can just hide it. If you upgrade to Catch Responsive Pro version, then you can remove the search box and add other widgets in that area too. Check out Pro version Details here and its Theme Instructions with features list here.
To hide search box and reduce top margin, try adding following code in Appearance=> Customize => Theme Options => Custom CSS Options box:
/* Remove Search box from header right area */
.sidebar-header-right #header-right-search{
display: none;
}
/* Reduce Top margin */
#masthead {
padding: 10px 0;
}
You can even reduce the 10px in code block /* Reduce Top margin */ to reduce it even more.
Let me know if it worked or not. If this does not work, you will need to post in your site url.