It all depends on the weather. With calm stable weather, you might be good for days. But if a weather system is moving in, your calibration may only be good for hours, maybe even less.
With a good recent calibration, you should be able to get altitude to within 10's of feet, or better, from a pressure based altimeter. That can easily degrade to 100's of feet due to atmospheric changes throwing off the current calibration.
Pressure sensors are also sensitive to temperature. But all we want is pressure. Therefore, the effects of temperature must be taken into account and corrected. Thus a separate temperature sensor is typically located near the pressure sensing element. That temperature is then used to compute a corrected pressure value. This correction can be quite complex.
Typically, the value from that temperature sensor is made available. But keep in mind that what it is providing is the temperature of the sensor itself.
Not reliably. Since the pressure sensor is relatively small (small thermal mass), it will change with air temperature and thus give a general indication. But it is, by necessity, buried down in the sensing element itself. So due to local self heating and other effects, it can be off by many degrees.
A decent and properly calibrated pressure altimeter will easily beat a GPS based altitude. Here we are only considering the GPS altitude derived directly from a 3D lock on multiple satellites, which is what a basic hand held GPS unit, or smartphone, will provide.