A faulty alarm is not an uncommon problem on an older car, and the circumstances you have mentioned are typical causes of an alarm going off incorrectly. Ultrasonic interior sensors monitor the movement of air within the interior in order to detect a door or window being opened, but can be fooled by the interior heating up as the external temperature increases. Similarly the boot open warning light suggests that the detector or the boot latch itself is faulty, and this would be enough to trigger the alarm when parked.

When locking the vehicle, if you press the lock button once this should arm the external alarm but not the interior sensors, which should prevent the external temperature causing the alarm to sound, or you can lock the vehicle with the key rather than the fob although this would mean the alarm is not activated. Fixing the boot latch should be sufficient to stop this cause of false alarms - lubricating the locking mechanism may be sufficient, but also check the wiring that runs between the bootlid and the body, as damage to this can cause errors. If this is unsuccessful you may need to replace the boot latch assembly.