Does the alarm output mean to be 5 V rising edge of falling edge and how much power does this chip consume.
Read the data sheets. The INT0 input needs a level change to wake the chip from sleep.
The chip uses a maximum of 25.6 (2V) or 86 (5V) microamps when keeping time. If keeping time with the battery it uses 0.4 microamps. I guess that means you can use an output pin to provide power to the chip when awake, then go back to battery power when the ATmega powers down.
I am also looking to switch the current to another device using relay functionality. And the relay would be turned on once the microcontroller comes back to sleep. I have checked out the basic circuits one given in the arduion play ground. I am unable to guess where would I place the positive and ground connection of the device which i need to run from the relay.
Driving a relay takes a good deal of power. Are you saying you want the relay to stay activated even after the ATmega goes back to sleep? I would think you'd want to use a latching relay for that so you don't use power just to keep some contacts closed.