Is the signal only executed once the signal is delivered to Telegram? What happens with the signal if the phone has no network or no battery?

Anny is a 24/7 cloud-based bot that doesn't require installation on a mobile phone or other devices. A slow connection can actually generate latencies in message delivery.

The delivery of the message to the user does not interfere with Anny's communication with Binance and the execution of automatic trades.

In other words, this means that your connection (or the state of your mobile phone - on or off) will not interfere with your performance on automatic trades.