I got the Arduino Uno. As I understand, the Vin pin can be used to power the Arduino using a battery pack with voltage above 5V right? What is the exact voltage range?
Then, the 5V pin can be used as an output to apply 5V at a logic pin of a stepper driver board that needs 5V, right? What is the current limit?
7v to 9v is a reasonable range that can be applied to Vin.
Voltage from the Arduino 5v pin can be used drive external circuitry but you must not draw too much current from the pin.
Suggest you keep current draw under 100mA.
The 5V pin is either powered via the voltage regulator in which case the current limit is around 100 mA (as mentioned before). Or it is directly connected to the USB in which case the polyfuse on the Arduino limits it to 500 mA (see the Uno schematic).
In my experience at least 6.7V to get proper regulation - though that depends on the exact regulator on the board you have.
The on-board regulator will dissipate heat equal to (Vin - 5)x current, so if you use
7V in you can draw more current than if you use 12V in - the regulator should simply shutdown if it gets too hot, but this is a limitation that can often bite people.
If you have lots of current draw in your circuit either use an external 5V regulator (on a heatsink?) or power from a suitably powerful 5V supply in the first place.