Beep using buzzer just when battery died or 5V connection died using capacitor
Is it possible i can use capacitor say 1 Farad which when battery died will discharge and made a beep (2 small beep will be good for identification) for a second and then everything is dead.

Yes it is possible.
You won't need a whole 1 Farad. This buzzer for example says 1V-30V and 5mA at 9V. If we guess that it can go down to 1V, from 5V, over 1 second, using 5mA, then the capacitance you need is:
$$C = \frac{Q}{dV} =\frac{5mA\cdot1s}{4V} = 1.25 mF$$

Some concerns were:

Is these cheap buzzers have any affect if it put them on opposite direction


I would not make current go the wrong way through a buzzer. It might work for your buzzer, or it might not. Maybe they make buzzers where it works. I wouldn't try it, unless I can replace the buzzer if it breaks.
You can use diodes so that current only goes the right way through the buzzer.
Or, since you have an Arduino already, why don't you make it so the Arduino is powered by the capacitor and the Arduino has an input which tells it when the power is lost?


Does they get impacted if the electricity comes back while it is being discharged


See above.


The capacitors does not charge linear i.e their voltage drops will that be too bad for my buzzer


It depends. You will not break the buzzer if the voltage is too low, but the sound might be wrong.