I guess it's all in the title. When using Vin as input, does it go through voltage regulator, or must I feed it precisely 5V?
If you look at the schematic you'll see Vin is connected to the input of the voltage regulator. Just like the barrel-jack (except for the diode).
So the same input-voltage of 7-12V applies to Vin.
when you connect you regulated 5V at Vin port your 5V output will be lower than 5V as it have to pass through the 5V regulator. The input voltage should range from 7-12V.