1. I cannot translate “Shipping and Handling” text on the checkout page. I have translated all other terms, including this one, in the .po file, just like in your instructions, but this term will not translate in the website. What could be the problem?
2. In my website there is no title for Payment methods, the payment methods simply appear after the totals.
1) to change this text you need to edit file \legenda\woocommerce\cart\cart-shipping.php (line 22)
Do not forget to make backup of file before editing!
We recommend you to make all changes to theme files only in child theme: https://codex.wordpress.org/Child_Themes
2) please provide us with admin credentials for your site in private content.