AFAIK, borrowing money does not change Equity, because it increases Assets (more money in the bank) and Liabilities (more debt) by the same amount so Equity stays the same.
1. Profit/loss measures changes in equity resulting from operating activity, as opposed to financing activities (which just rearrange how the company is financed).
2. Examples of financing activities are taking out (or paying back) loans, issuing (or buying back) shares, and issuing dividends.
3. Some (not all, as you point out!) of those financing activities will increase or decrease equity. So, when thinking about profit as the rate of change of book value, you should be careful add back any changes that are the result of financing activities. (specifically: ignore changes in equity due to money going to, or coming from, shareholders)
Not until the interest accrues. You could (no idea why you would) borrow $1MM and immediately pay it back before owing any interest. You would need to reflect this on your books but nothing material has changed.
> You could (no idea why you would) borrow $1MM and immediately pay it back before owing any interest.
Can you in fact do that? It's possible with a residential mortgage in the US, because there are laws prohibiting prepayment penalties. And I think even those don't apply to refinanced mortgages?