Note that the schematic is not complete. Several current limiting resistors are missing. Also, the diodes can be replaced with 1N914, 1N4148, etc.
1. 4N35 or similar general purpose optocoupler. Add a diode in reverse parallel across the input diode and a series resistor to limit current to 10 mA.
2. Depends on the solenoid power. Non-repetitive peak current rating is 800 mA, but repetitive current is only 2 mA. Probably need another TRIAC.
3. The circuit does not show the relationship between either AC power let and the circuit GND, so this is not perfectly clear. The long way is to add another 555 configured as a monostable, triggered by the back door button, and connected to one of the output optos with another diode.
ak