Hi @neovlademarvel,
You should be able to display shipping/taxes and any extra fees that might be added to the order using the WC hook woocommerce_email_order_details
as
do_action( 'woocommerce_email_order_details', $order_obj, $sent_to_admin, $plain_text, $email );
in the PHP email template.
The best way to currently modify the email template is to customize it.
Please copy the email template using the WooCommerce->Settings->Emails->Send Quote->Copy file to theme button into your theme folder. Once done, you can customize the email template as desired.
Updating the plugin to future versions will ensure that the customized copy is not overwritten.
So, you would have to remove all the HTML that is present in the send-quote.php file with regards to the cart table and replace it with the hook I mentioned above.
I have created an example file for you which you can access here.
Thanks,
Pinal