So say you want to use transistors with your Arduino Nano to power components, which require greater than 12V. If your power supply is more than 12V, is there a way to safely use the same power supply to power the Arduino?
The voltage regulator (on the Vin pin) is supposed to be provided with 12V at max, since it is not cooled (it is a linear regulator, that dissipates the excess voltage as heat). If you have significantly more, you should at best buy a little switching regulator, to directly get a regulated 5V to feed to the 5V pin of the Arduino (that's what I suggest). Be sure to use a regulator, that can provide the needed current (which also depends on what else you provide over the Arduino).
If you really don't want to use an extra regulator and you don't have much more than 12V (maybe like 15V), you might get away by cooling the voltage regulator on the Arduino. The voltage regulator on a genuine Arduino will go into emergency shutdown, if it overheats, but it will not be damaged easily. Here you could try a bit. But be careful to not stress it too much. The clones from china often have different/cheaper regulators, that will mostly be fried if you overheat them. But they are very cheap.
The recommended input voltage for the Arduino Nano is 7-12 V, the max. 20 V.
So you could use upto 20 V, but this is indeed not advisable.
What you can do, is to use a so-called step down/boost down converter which converts the voltage back to a voltage that your Arduino Nano can (easily) handle. The voltage drop will be changed into heat, but I guess considering you are using a higher voltage power supply, you are not using battery power.
Note: this is only true for some (cheap?) converters, see the comment of DataFiddler below.
If I understand your question you have external devices say lamp, motor, etc. There are several ways of doing it. My preferred way is to use a N-Channel MOSFET where the drain is the output, the source is ground (both the logic and power grounds need to be connected together) and the gate Is connected to the port pin that also has a 10K pull down resistor. You can use the 12V to power the Arduino via Vin as you suggested. Be sure the MOSFET is avalanche rated and will turn on at about 3V or less.
You can do the same thing with an NPN Transistor where the port pin connects to the base with a 300 Ohm resistor (you need to calculate this based on the load), emitter to the connected grounds and the collector is your output.