Yes trade stays open until you receive payment. Once you see it in your bank account you confirm that you have received it and you release crypto to seller. You should also make sure that he does not pay you from a third party account and if he does I'd recommend to send it back and cancel the trade.
No that's︃ not true. Those timers on binance P2P are wrong. Trade stays open until you confirm︄ that you received payment. I'm merchant on binance P2P and in some extreme cases I︅ had a trade open for longer than month.