Remove search box on left on all blog pages

That’s a default for Secondary Sidebar when there is not widget in it.

Try dragging some widgets into Secondary Sidebar, the search box should be gone.

So it’s the removing the left sidebar, not just the search box.

I looked into theme files and found that it’s less complicated to do this than I initially thought. It feels like the CSS is firstly prepared for no left sidebar and the image size added in function too.

The header of your child stylesheet shown above is missing the @import line, could be that you only show the top part, but anyway you must have the @import line in it.

/*
Theme Name:     Ascetica Child
Theme URI:      xxx
Description:    Child theme for the Ascetica theme
Author:         Rachel Johns
Author URI:     xxx
Template:       ascetica
Version:        0.1.0
*/

/* ===== Import parent's style ===== */
@import url("../ascetica/style.css");

/* ===== make no left sidebar  ===== */
#content {
	margin-left: 0;
	width: 100%;
}

#sidebar-secondary {
	display: none;
}

With that and also put an empty Text Widget into that sidebar, to get rid of the default search box in the markup.