1. I believe the 555 is rated to 15V, check for yourself, but I am almost certain that it is, so you dont need to drop the voltage to 9 volts first.
2. Triacs have a minimum gating current. The gate looks like a forward biased diode, so you need to figure out what the gating current should be and put an appropriate resistor between your trigger and the triac gate pin.
3. Most triacs I have used have pins 1 and 2 as the AC and pin 3 as the gate in a TO-220 package.
4. Your transforer has a center tap, so its DC output is 12-0-12. You could use just the two like colored wires to get 24V, use the two like colors in parallel to get 2x as much current at 12V, use only one side to get just 12V.