Can I run 3 devices on Arduino Uno with different power sources?
Your question is 2 fold:


Power requirements: The actual power requirement depends on the devices, but the Arduino will certainly not be able to provide power for a heating lamp. It just cannot provide that much current (you would fry the Arduino). But the Arduino is also only powered from outside. I guess you have a power source, that can provide enough power for all the devices. Then you can connect these devices in parallel to the power source (meaning + and - of the heating lamp power goes directly to the power supply). That way the current for the devices doesn't flow through the Arduino. The Arduino will only use control signals, which don't have high current. Sensors are normally either analog sensors (which connect to the analog pins with only neglectable currents) or use communication interfaces, which are also ok. The current hungry output devices (humidifier and heat lamp) either have a digital control pin, a communication interface, or they must be controlled via a relay (depends on the actual devices).
Controlling all the devices: The Arduino can only do 1 thing at a time. But that is no problem, since you can do things sequentially very fast. For example write one function for every device, that you want to control. In that function you communicate with/control the device according to some variables (like the measured temperature). The loop() function can then look as simple as:

void loop(){
    measure_temperature();
    measure_humidity();
    measure_soil_hydration();
    control_humidifier();
    control_headlamp();
}


If you want to only do this periodically (not all the time), you can either add a delay() or - better - use millis() like in the BlinkWithoutDelay example (there are also many tutorials about millis() on the web). Make sure, that the individual functions are not blocking. They should do, what they need to do, and exit quickly. No long staying in loops or waiting for an event there.