I want to make an incubator. So I am using W1209 thermostat. I want to control AC and DC. I can control AC (220v AC) by the relay output. Can I control DC by connecting DC directly from the relay input (12v DC)
Note that while Q1 is switched off there is 12 V at both sides of the relay coil. That is probably not what you need.
It could be worse than that: at the moment that Q1 is switched off, there will be a bit of a voltage spike which could (unlikely, but I haven't done the calculations) go through your other 12 V DC circuit and destroy it before the diode helps diminish that spike.
How to make it work.
Refer to the STM8S003F3 datasheet.
Once you have consulted the datasheet to find how much current can be sourced from pin 10 of the IC, you can determine if it would be better to use one buffer (to go to the 12 V DC control circuitry) attached to pin 10 of IC1, so that the maximum output current is not exceeded, or if pin 10 can't cope then two buffers where the additional one is put between pin 10 and R7.
If this device already controls 220 V AC via a relay, then you can control anything else with a 220 V relay. That's better than breaking into devices that you don't really understand.