Yes, on the site settings tab, you should enter the https address for your site.
No, the incontext option is only available for the US paypal API, it is not availbale for the UK API.
Yes, for the order information, you should use the eCart Checkout Form in the Dynamic Data list. if you have columns in your order table to store the billing info, use the billing form elements, columns for the shipping info should use the shipping element bindings.
for the order details bindings issue, try toggling the connection to none, then reselecting your connection.