Let me suggest to connect direct to pins 0 and 1 instead.
Then try below code and see if you get a reply OK from the phone.
void setup() {
Serial.begin(9600);
delay(3000);
}
void loop() {
Serial.println("AT"); //Asking the phone if the connection is working
delay(3000);
if (phone.available()) {
Serial.print((char)phone.read());
}
if (Serial.available()) {
phone.print((char)Serial.read());
}
}