The two questions are solid, but they ask “is it a number?” — and some labels are written as numbers just to fool you. Here's how to see through the costume.
Numbers That Are Really Categories
A postcode is 2000. A jersey number is 7. A phone number is a long string of digits. They're written as numbers, so “is it a number?” tries to say numerical — but think about what the number does. Postcode 2000 isn't twice as much as postcode 1000; it's just a name for a place that happens to be spelled in digits. The real test isn't “does it look like a number?” — it's “can you sensibly do maths on it?” The average of two jersey numbers is meaningless. So postcodes, jersey numbers and phone numbers are all categorical, every time.
Ordered Labels Hiding in Plain Sight
Some categories aren't just buckets — they come in an order. Small / medium / large. Cold / warm / hot. Disagree / neutral / agree. These are still categorical (you can't average “medium”), but unlike eye colour they have a built-in ranking. They get their own name — ordinal — for exactly that reason: the order carries real meaning, even though there's no number underneath. Plain unordered labels like eye colour are nominal; ordered ones are ordinal.
Age, the Famous Trick
We say “I'm 13,” a whole number, so age looks discrete. But age is continuous — you are constantly, smoothly getting older; right now you're 13 years, some months, some days, some seconds. We just round it down to whole years because that's convenient. Rounding a value for convenience never changes its real type. Height rounded to the nearest centimetre is still continuous; age rounded to whole years is still continuous. The type lives in how the quantity behaves, not in how neatly we wrote it down.
A Worked One, Slowly
Is a student's ID number numerical or categorical? It's written as a number, so the lazy answer is “numerical.” But run the real test: would averaging two student IDs mean anything? No — ID 4071 isn't “more” than ID 1207, it's just a name in digits. So it's categorical, same family as postcodes and jerseys. Costume off.