Hi there! Yes, you can use CSS and basic WordPress functions in a child theme to do this. I recommend using Firebug for CSS work--makes it much easier.
You'd want to target the
wp-post-image class in your child theme's style.css and set the
border-radius property to 0.
To make the featured images larger, you'll need to create a new functions.php file in your child theme and overwrite set_post_thumbnail_size() with the dimensions you'd prefer. Hook this into
after_setup_theme like so:
set_post_thumbnail_size( '150', '150', true ); //change the values to whatever dimensions you want
add_action( 'after_setup_theme', 'child_theme_thumb_size' );
To add them to the archive pages, you'd look at the code in index.php for adding the post thumbnail, then copy and paste that code into a new copy of archive.php in your child theme.
I haven't tested this, so you may need to play around with it a bit to get it to work for you.