For featured image size you can add this to your theme’s function.php (Make sure you backup first and havea child theme)

if ( function_exists( ‘add_theme_support’ ) ) {
add_theme_support( ‘post-thumbnails’ );
set_post_thumbnail_size( 150, 150, true ); // Change to your desired image size
}

To make a custom page you can check out this tutorial by https://www.wpbeginner.com https://www.wpbeginner.com/wp-themes/how-to-create-a-custom-page-in-wordpress/
They have a video so you can easily follow it.

To assign a page as your homepage goto your dashboard > Settings > reading https://prntscr.com/i5xp1k
In the reading page, look for the dropdown field “homepage” this is where you can choose which page you want to be your homepage https://prntscr.com/i5xqwu