Maybe you are right but only if the recipient keeps it in the bank account without spending it or withdrawing it. I once received some money in a bank account without knowing who the sender was, only a few minutes the bank withdrew the money and my balance returned to normal.
Sure, because the bank is a centralized institution and the money in your account is under their control, not yours. If a bank mistakenly deposits money in to your account, then again, no money has actually moved anywhere; all that has happened is that the bank have mistakenly updated your entry on their database to show more money than you have. If you had withdrawn that money before the bank realized their mistake, then they simply would have deducted the respective amount from your remaining balance. If you had no balance remaining, then they would have come after you for outstanding debt.
With bank transfers, credit card payments, PayPal payments, etc., you can reverse the payment for up to 180 days after it has been made. It doesn't matter if the recipient has withdrawn that money and spent it already - the bank will simply take the money from the recipient's other balances or accounts. They are in control, not you.