What is the power requirement for switching this relay?
Q1. The Arduino will go up in smoke if you put 12V onto one of it's port pins.
Q2. According to the link you provided, the board can accept a 'LOW' input of 5V. This would seem to be the suitable one.
The information is scant which makes it difficult to give a precise answer. Given that there is optocouplers on the board, the Arduino can easily drive these. There seems to be a COMmon pin which would connect to the Arduino 0V and the Arduino port pins would connect to the requisite CH1..4 input on the relay board.
Unfortunately there's a number of these relay boards and they're not all the same - I usually sketch out the schematic to understand how they work.