Circuit with 7812 and 7805 for power supply

So guys, nowadays I am thinking of designing a circuit with 7812 and 7805 for power supply. I will connect 7812’s input to output of bridge which will be 20V and I will connect input of 7805 to output of 7812. I will use good heatsinks for L200, 7812 and 7805. Actually the 7805 will be driving PIC12F, a 3mm LED @ 10 mA and base of transistor @ < 5 mA. The 7812 will drive a relay which draws 150 mA.

So is my Circuit correct? Can I connect 7812 to the output of 1N4001 in the L200 based circuit and can I also connect 7805 to the output of 7812? I want to know if the 7812 and 7805 heats up or not. 7805 will power a PIC12F683 and 12V is used to drive a buzzer and a relay.

And what about Vin to LT1083 ? The datasheet says its input should be 25V or more, so can I input 28V into the LT1083 and take out 12 V ?

I am driving a solenoid valve. Earlier I used a valve whose current rating was 150 mA @ 12V. Now I am using a better quality valve at its current rating is 2A. So, I will be using LT1083MK-12 to power the solenoid valve. Should I use LT1083MK-5 to get 5V for PIC circuit ? PIC circuit will not draw more than 100 mA.

I am asking this because I have a 8051 dev board and it has a 12V 500 mA adaptor and the board has a 7812 regulator with good heatsink. If I use 12V 500 mA adaptor with the board then everything is ok but if I use 12V 2A adaptor then within 15 to 20 seconds the 7812 heats up very much. I don’t know the reason. I think it is due to high current adaptor.

That’s why I am asking if it is ok to use a 7805 when input is 12V 3A. I know that only if the circuits (load) draws current then the regulator will deliver that much current but why in my dev board the regulator heats up if 2A adaptor is used ?

I am also going to use a 400V 6A diode in reverse across the solenoid coil which is rated at 12V 2 A.

It is for a Gas Leakage detection system where if LPG gas leakage is detected it will close the valve and shut of the gas flow. It is a NO type valve and hence I am using a battery so that if there is a power failure and also if there is a gas leakage then power is needed to close the valve. Battery will be 12V 10Ah Gel battery.

Finally I just want to know is it Ok to use LT1083MK-12 to power the solenoid and buzzer and LT1083MK-5 to power the PIC12F. Earlier there was an LED in PIC circuit which was used to display status that is the LED would blink once every time the while(1) loop got executed but now I removed it and hence 10 mA current consumption is also saved. I have used that pin to monitor mains voltage using ADC pin. If mains voltage goes below 180 V the PIC will turn OFF a relay and hence connect battery power to circuit and valve. If mains is ok then relay will be ON and battery out is cut off.

Ps: The reason I am not using a NC valve as everybody would do is here power cuts are common and NC type valve closes if there is a power cut and I will have to use a battery to keep open the valve during these times. As solenoid draws 2 A current power consumption will be more.
So, I use NO type valve and only if gas leaks or if there is power cut with a gas leak then valve is operated and closed. Once valve is closed it remeins in that state and buzzer will be sounding. The leakage has to be rectified manually and then system has to be reset so that it continues functioning.

Thanks guys.