Is the repentance of one who has committed adultery and lottery accepted, and who feels deep remorse for his actions but has not yet wept, and is there a way for him to know if his repentance has been accepted?

Sincere repentance erases major sins. Weeping is not a condition for the acceptance of repentance; rather, its conditions are: abandoning the sin, regretting it, resolving not to return to it, and restoring rights to their owners if they pertain to a human being. Weeping out of fear of Allah is a sign of sincerity and faith, and Allah has praised those who weep out of His fear. As for residing in lands of disbelief, it is not permissible except under specific conditions.