Well the first question is how are you going to connect the Arduino to your gate, letterbox, PIR sensors, and weather sensors. Chances are, these are all going to be several dozen feet away from each other, correct? Do you want to run wires through walls/underground or do you want to go wireless?
As for writing to MySQL, check out this thread: http://arduino.cc/forum/index.php/topic,37718.0.html