If he loses his job or source of income, yes, he is.
Exactly. Conceivably, one could have an annual salary of $500,000 and be considered "poor", using this definition.
As always, there are lies, dammed lies, and statistics.
It depends on how much the fancy house is actually worth. If he has $900,000 in the bank, owes two million on the house, and the house is only worth a million, assuming all his other assets and liabilities net out to zero, he is worth -$100,000. If the house is worth three million, then he is definitely rich, with a net worth of $1,900,000.
The person with a negative net worth may be materially comfortable, but is vulnerable to things such as inflation or loosing his job. Walking away from the debt may or may not be a good option. This can be a psychological burden, and may be a real problem when the house of cards collapses. Still, it is very different from wondering what one will eat tonight.