I cannot find option to modify my post excerpts

It takes a while ..go on read.
Create a child theme and create a folder parts in child theme
1)Currently it is

This entry was posted in category and tagged tags on date by author.

if you want to change as above
copy the class-content-post_metas.php in parts folder of parent theme and paste it in the child theme go to lines 76-82 where it says

if ( $tag_list ) {
                $utility_text   = __( 'This entry was posted in %1$s and tagged %2$s on %3$s<span class="by-author"> by %4$s</span>.' , 'customizr' );
                } elseif ( $categories_list ) {
                $utility_text   = __( 'This entry was posted in %1$s on %3$s<span class="by-author"> by %4$s</span>.' , 'customizr' );
                } else {
                $utility_text   = __( 'This entry was posted on %3$s<span class="by-author"> by %4$s</span>.' , 'customizr' );
            }

those are the culprits change them to your wish. like you asked

if ( $tag_list ) {
                $utility_text   = __( 'This post was created in %1$s on %3$s<span class="by-author"> by %4$s</span>.' , 'customizr' );
                } elseif ( $categories_list ) {
                $utility_text   = __( 'This post was created in %1$s on %3$s<span class="by-author"> by %4$s</span>.' , 'customizr' );
                } else {
                $utility_text   = __( 'This post was created in %1$s on %3$s<span class="by-author"> by %4$s</span>.' , 'customizr' );
            }

2) check this
http://codex.wordpress.org/Function_Reference/the_excerpt#Make_the_.22read_more.22_link_to_the_post

To do that create a new file functions.php(be careful!) in child theme and add

function new_excerpt_more( $more ) {
	return ' <a class="read-more" href="'. get_permalink( get_the_ID() ) . '">   Read More</a>';
}
add_filter( 'excerpt_more', 'new_excerpt_more' );

Don’t want to link title to post then, add copy the file class-content-post_list.php and add it to the child theme got to lines 113 -120 where its says

if ((get_the_title() != null)) {
                      printf(
                          '<h2 class="entry-title format-icon">%1$s %2$s</h2>' ,
                          '<a href="'.get_permalink().'" title="'.esc_attr( sprintf( __( 'Permalink to %s' , 'customizr' ), the_title_attribute( 'echo=0' ) ) ).'" rel="bookmark">'.((get_the_title() == null) ? __( '{no title} Read the post »' , 'customizr' ):get_the_title()).'</a>' ,
                          //check if comments are opened AND if there are comments to display
                          (comments_open() && get_comments_number() != 0) ? '<span class="comments-link"><span '.$style.' class="fs1 icon-bubble"></span><span class="inner">'.get_comments_number().'</span></span>' : ''
                      );
                  }

and change it to

if ((get_the_title() != null)) {
                      printf(
                          '<h2 class="entry-title format-icon">%1$s %2$s</h2>' ,
                          get_the_title() ,
                          //check if comments are opened AND if there are comments to display
                          (comments_open() && get_comments_number() != 0) ? '<span class="comments-link"><span '.$style.' class="fs1 icon-bubble"></span><span class="inner">'.get_comments_number().'</span></span>' : ''
                      );
                  }

3)It is possible..copy the index.php file and paste it in child theme
go to line 21 where it says
<div id="content" class="<?php echo tc__f( '__screen_layout' , tc__f ( '__ID' ) , 'class' ) ?> article-container">

just below that add
<h2>Latest Posts </h2>

4)You can set featured images while writing the posts ..if it isn’t there then theme checks for images uploaded to the post and displays it.Those circles are just styles applied to it.

Do it carefully if you get any error just revert back to the parent theme.

#1 It seems you didn’t add the code correctly.

#1 Got it.As you are using home page for blog posts it is not displaying category ,author,date.

To get that on home page copy class-content-post_list.php (if you haven’t) into the child theme
go to lines 123-127 where it says

<?php //meta not displayed on home page, only in archive or search pages
                      if ( !tc__f('__is_home') ) {
                          do_action( '__post_metas' );
                      }
                  ?>

change that to

<?php 

   do_action( '__post_metas' );
  ?>

4)No circles for thumbnails:
GO to line 326 in class-content-post_list.php where it says
$html .= '<a class="round-div '.$no_effect_class.'" href="'.get_permalink( get_the_ID() ).'" title="'.get_the_title( get_the_ID()).'"></a>';

Change that to
$html .= '<a '.$no_effect_class.'" href="'.get_permalink( get_the_ID() ).'" title="'.get_the_title( get_the_ID()).'"></a>';

No need to change that ..Read my other post http://wordpress.org/support/topic/i-cannot-find-option-to-modify-my-post-excerpts?replies=9#post-4943850

Oh! you forgot to wrap that in php , add the following instead of that

<?php
function new_excerpt_more( $more ) {
	return ' <a class="read-more" href="'. get_permalink( get_the_ID() ) . '">   Read More</a>';
}
add_filter( 'excerpt_more', 'new_excerpt_more' ); ?>

It seems you are using manual excerpts.
If you are using manual excerpts , add this in functions.php

<?php

function excerpt_read_more_link($output) {
 global $post;
 return $output . '<a href="'. get_permalink($post->ID) . '"> Read More...</a>';
}
add_filter('the_excerpt', 'excerpt_read_more_link');

?>