1.If a ac signal is passed it will to pass right like an resistor.
2. If a pulsating dc as in case of o/p of bridge rectifier, it has freq also. In this case it don't act as resistor but it will charge or discharge right?

3. We say ceramic have lowest ESR, then tantulum or electrolytuic. Lower the ESR, more current it will leak, isnt it. Then why to prefer ceramic

 

1. An AC or pulse signal will pass through a series capacitor with the capacitor having a reactive impedance (not resistive) that is inversely proportional to the signal frequency components and the size of the capacitor.

2. If the capacitor is connected to ground (common) then it passes the AC frequency components components of the pulsating DC to ground and stores the DC component, thus acting like a filter.

3. ESR is the Equivalent Series Resistance and is unrelated to capacitor leakage current, which is a different parameter. The ESR dissipates power which can cause the capacitor to heat up in high current applications and also makes the capacitor less ideal.

I suggest you read up on capacitors such as here, to get a better understanding.