Vin goes through the voltage regulator and with an Arduino Uno or Mega, Vcc will be 5V.
...Nothing in the analog world is "exact".
You have to careful about how much "stuff" you power through the built-in voltage regulator. The heat (or energy wasted as heat) in regulator is a combination of the current through it and the voltage dropped-across it. So the higher the current and/or the higher the voltage, the more you are stressing it.
Ambient temperature also contributes. I think it has over-temperature protection so it should shut-down instead of burning-up and dying.
It is a physical impossibility to generate a voltage (or anything else) to be 'exact'.
If you provide a supply within the specified acceptable range and keep the load under the specified acceptable maximum load then the output voltage will be within the specified output voltage range. Read the datasheet for the voltage regulator on the board.
Read the data sheet for the particular manufacturer's part, it will give you the tolerance. Be sure you follow the correct one as they can have several with the same part number but a different letter. Also how many places right of the decimal are you talking?
Yes, 5volt does not depend much on V-in supply voltage.
The 5volt regulator tries to keep it within it's tolerances.
But there is another problem.
12volt on V-in is nearing the danger zone for a classic Nano. At that voltage you can't power anything from any pin, apart from sensors that run on fumes. Be prepared to see sparks if you increase that to 18volt.
Leo..
That table doesn't mention the ~50mA current draw of an Uno, so that 85mA becomes 35mA.
Practically it isn't that bad with an Uno with a large USB socket, because that also becomes part of the heatsink. A classic Nano draws about 30mA, but it could be worse, because it has less copper to dissipate the heat.
Leo..
That depends, unfortunately, on the particular LCD, as various products will draw (slightly) different currents. The best way to find out is to measure the current going in to Vin with
a) just the Nano
b) Nano and LCD
That will allow you to calculate the current the LCD needs. However, at that point, you know the total current being drawn, and can therefore determine from the chart previously mentioned), whether you're at risk or not.
If you could drop the 12V to 7V, that would improve the available current for other devices, including your LCD. That would best be done with a "buck converter" set to 7V output.
but then again, why not just set the buck converter to 5V and bypass the onboard regulator. It's pretty much useless at that point.
I personally would not use the on-board regulator, I prefer to use a 5V supply for everything. However, I think @camsysca has given you a much better answer than I can.
Nice explanation, I am assuming this is at a 25C ambient.
I prefer to use Vin for the additional filtering etc that it offers. I power Vin with 7.5 to 8V. Parts that need 5V over 10mA are powered by an external power supply. I am from the automotive world and any help is generally used.