I do have a child theme. I spent over an hour one day setting it up.
As to which themes contain the same information, take your pic. Mog includes publish date, Responsive has date and author, Spun, Stitch, any of them on the first page when you select themes.
I figured out the first part by playing around with it and teaching myself PHP so far. I deleted this section of code from the content-single.php file:
<div class="gj-article-details"><dl class="gj-article-info"><dd><?php _e( 'Date: ', 'preference' ); ?><?php the_time(__('F j, Y', 'preference') ); ?></dd><dd><?php _e( 'Author: ', 'preference' ); ?><?php the_author(); ?></dd><?php edit_post_link( __( 'Edit', 'preference' ), '<dd class="edit-link">', '</dd>' ); ?></dl></div>
For modified:
<?php the_modified_date( 'F j, Y', __( '<span class="modified-date">Last Modified: </span> ', 'preference') ); ?>
</footer><!-- .entry-footer -->
For posted in:
<?php $categories_list = get_the_category_list( _x( ', ', 'used between list items, there is a space after the comma', 'preference' ) );$tags_list = get_the_tag_list( '', _x( ', ', 'used between list items, there is a space after the comma', 'preference' ) );if ( $categories_list )printf( '<span>' . __( '<span class="cat-links">Posted in: </span> %1$s.', 'preference' ) . '</span><br />', $categories_list );if ( $tags_list )printf( '<span>' . __( '<span class="tag-links">Tagged: </span> %1$s.', 'preference' ) . '</span><br />', $tags_list );?>