When the escape velocity from EH is c, then how can Hawking radiation escapes it? Does it travel faster than c? Or, it escape from outside the EH? If so, how a BH can evaporate beyond EH?
In quantum field theory, particle antiparticle pairs spontaneously pop out of the vacuum all the time, essentially borrowing energy from the vacuum and then subsequently annihilate each other.
However, when an event horizon is present, you can get situations where the pair is generated very close to the horizon. If the pair is generated such that they both are highly energetic, but one particle happens to be just inside the horizon whereas the other is just outside the one that is outside will fly away since even if you are just outside the horizon it is still possible to escape. No particle here goes faster than light or crosses the event horizon in the wrong direction.
Please note that this is a very commonly asked question, such as here From where (in space-time) does Hawking radiation originate? (you should check out some of the answers there, some are of much higher quality and greater depth than my own).
Please try to do research before you ask!
Edit answering why this causes the BH to lose mass
Contrary to your intuition, the black hole has lost a particle's worth of energy since the energy to create the pair came from the spacetime on or around the event horizon, so really energy was borrowed from the event horizon to create the pair but it only got one particle back so the black hole was 'short changed'.