Hello,
1) Have you set “Enable the shipping calculator on the cart page” http://prntscr.com/p09ji2 > http://prntscr.com/p09jcb in WooCommerce > Settings > Shipping > Shipping options?
Isn’t this what you are looking for?
2) http://prntscr.com/p09kzq https://docs.woocommerce.com/document/free-shipping/
Your questions relate to WooCommerce plugin functionality, so it would be better to ask them on forum of the WooCommerce (we are theme support).
Regards