controlling AC using arduino

if i want to control an 220V Air conditioner on/off using arduino, do need a contactor together with a relay?.. or this relay is enough?

Depends on the AirCon unit - what’s its current, is it inductive? Inductive ratings and resistive
ratings are very different, you’ll need to check what your relay can handle inductively if the AirCon
uses induction motor (likely). Usually a snubber network would be used in this situation to
prevent the relay contacts being welded shut.

"5V 2-Channel Relay interface board, and each one needs 15-20mA Driver Current
Equipped with high-current relay, AC250V 10A ; DC30V 10A
Standard interface that can be controlled directly by microcontroller (Arduino , 8051, AVR, PIC, DSP, ARM, ARM, MSP430, TTL logic)
Indication LED's for Relay output status"

-Amazon Listing
A) It says it works with a 5V trigger (perfect for using with the Arduino)
B) It says it works with AC250 10A, If you only are relaying AC220 and under 10A it shouldn't have any trouble.
C) It depends on what you are relaying. If you are doing a pow cable splice you are probably good. If you're going inside you'll need more information to be sure. It also depends on how long the relay will be active with current flowing through it. The longer current is flowing the more stress it will be put under.