To change title from h1 to h3, you need to replace the following code
<h1 class="page-title"><?php printf( __( 'Search Results for: %s', 'catchkathmandu' ), '<span>' . get_search_query() . '</span>' ); ?></h1>
with
<h2 class="page-title"><?php printf( __( 'Search Results for: %s', 'catchkathmandu' ), '<span>' . get_search_query() . '</span>' ); ?></h2>
Then to remove the image from the search, you need to copy content.php file and then replace
<?php if ( function_exists( 'catchkathmandu_content_image' ) ) : catchkathmandu_content_image(); endif; ?>
with
<?php if ( function_exists( 'catchkathmandu_content_image' ) && !is_search() ) : catchkathmandu_content_image(); endif; ?>
then to change the post title from h1 to h3. replace the following code from content.php
<h1 class="entry-title"><a href="<?php the_permalink(); ?>" title="<?php echo esc_attr( sprintf( __( 'Permalink to %s', 'catchkathmandu' ), the_title_attribute( 'echo=0' ) ) ); ?>" rel="bookmark"><?php the_title(); ?></a></h1>
with
<h3 class="entry-title"><a href="<?php the_permalink(); ?>" title="<?php echo esc_attr( sprintf( __( 'Permalink to %s', 'catchkathmandu' ), the_title_attribute( 'echo=0' ) ) ); ?>" rel="bookmark"><?php the_title(); ?></a></h3>
.
