Because most websites won't have two separate fields for "ZIP code" and "postal code". Even if they knew that ZIP Code is a trademark (I didn't until you mentioned it), they would (wisely) know that putting in two fields would just confuse most people. So they put in one field. Many sites label it as "ZIP code / postal code", but some just label it as "ZIP code". But the intent is clear: put in the multi-digit string that identifies your address, whether your country calls it a ZIP code or a postal code.
Put country first. Postcode doesn’t make sense without one. Prepopulating one based on location is generally okay, but don’t assume it will always be the same.
