Is it forbidden to recite specific adhkar and awrad, such as Ayatul-Kursi and certain supplications, if the reciter intends to commit a sin? And by analogy, is it permissible for someone going to a place of sin to recite the dhikr for leaving the house, but he recites it for protection and not to seek aid for the sin?

Morning and evening remembrances (adhkar) are legislated to protect a person from Satan. However, remembering Allah with the intention of seeking help for a sin is forbidden. There is no blame on someone who regularly recites morning and evening remembrances while intending to commit a sin, as long as their remembrance is not an act of seeking help for that sin or during its commission. Allah may forgive the disobedient due to their remembrance, for "So whoever does an atom's weight of good will see it." And the remembrance upon leaving the house does not belittle the remembrance, even if one intends to commit a sin. A Muslim should be concerned about their own state and strive for sincere repentance and abandonment of sins.