But loans aren't typically available immediately - they take time to clear. It doesn't seem unreasonable to me that they'd bundle the day's loans (or maybe a few hours at a very large bank) to limit the number of transactions they'd have to make.
The money that gets borrowed from the Fed is used to settle balances between banks. When a bank originates a loan, they just add a number to an account. The money doesn't come from anywhere. This works mainly because most money transfers are electronic.
tl;dr yes, banks create money out of thin air. It's been this way for decades.
Ehhh, how does that work exactly? They go up to the discount window and borrow from the Fed every time they issue a loan?