Arduino Controlled AC Dimmer Circuit
1.You can use SCR/thyristor to control a AC load .The principle used is Phase angle control. Thyristor can control only one half of A.C.If you need a full cycle control , you can either use a Triac or Two SCR connected anti-parallel.
This link might be useful to know further.

2.The rms AC output depends on firing angle of the SCR.So if you want to control firing angle , you need to have a pulses of specific duty cycle to be provided to gate of scr using PWM technique from arduino digital pins.
This link can help.

3.If you use two SCR connected anti-parallel, there is no need of  commutation circuit.As they are automatically Commutated by Line commutation meaning during Natural AC reversal the opposite SCR switches on and present one switches off. As a thumb rule, AC to AC converters don't have commutation circuit.