Is a general repentance sufficient for someone who has committed adultery many times, or must there be a specific repentance for each instance? And what are the conditions for a sound repentance, and does it include the resolve not to return to the sin?

It is sufficient for the penitent to abandon the sin, regret it, and resolve not to return to it. If their repentance is sincere, Allah will forgive them. The conditions of repentance according to Ibn al-Qayyim are regret for the past, abandoning the sin in the present, and resolving not to return to it in the future. As for seeking forgiveness (al-i'tidhar), Ibn al-Qayyim views it as a demonstration of weakness and humility, and that it is a completion of repentance, being a display of submissiveness, neediness, acknowledgement of inability, and affirmation of servitude.