Mercy and justice are the two themes that play a huge role in this play. Where are these themes present and which characters are most affected by them?

The themes of justice and mercy come to the forefront in Antonio's trial. Shylock has taken Antonio to court because Antonio has failed to repay Shylock the money he has borrowed. In consequence, Shylock wants the right, as the contract stipulates, to cut a pound of flesh from Antonio's body. Shylock comes armed with a knife and plans to take the flesh from Antonio's heart. This is a death sentence, as, of course, nobody can live without a heart.
Shylock represents justice. He wants the letter of the law followed. Legally, he has a right to demand the pound of flesh, and he plans to get it.
Portia represents mercy when she disguises herself as a lawyer to represent Antonio. She gives an eloquent speech in which she says the "quality of mercy is not strained [over-used]" and pleads that Antonio be dealt with compassionately.
In the trial, Shakespeare plays on stereotypes that Jews like Shylock are legalistic and split hairs over "law," while Christians understand the sprit of the law and are compassionate and merciful, as Jesus commanded. Of course, Shylock is not dealt with very mercifully in the end by the Christians, though it is more merciful than how he wanted to deal with Antonio.
The two characters most impacted by the debate between justice and mercy are Antonio and Shylock. Interestingly, however, justice prevails in the court when Shylock refuses mercy: Portia is able to argue that according to the letter of the law, Shylock can only take Antonio's flesh but not his blood, which makes cutting a pound of flesh impossible. Shylock is dealt with harshly when justice prevails.