It's a difficult subject for me. When they executed people for adultery, blasphemy, murder etc in the Old Testament Jesus hadn't died and paid the penalty for sins then. 
Jas 2:10  For whosoever shall keep the whole law, and yet offend in one point, he is guilty of all. 
Jas 2:11  For he that said, Do not commit adultery, said also, Do not kill. Now if thou commit no adultery, yet if thou kill, thou art become a transgressor of the law. 
So does that mean that if you want to execute people for murder by God's law you also have to execute them for adultery or any law breaking offence? I feel that killing people in the Old Testament doesn't hold the same for today. Maybe I'm just being soft. I prefer prison sentences in my books 

I have murder etc in my book, it's a murder mystery so it's like the main subject, but justice will be seen to be done in the end. I guess in Elizabethan times punishments were far stricter than they are in this day and age, so I'm not sure how I'll deal with that. As long as justice is done I don't think it matters in what way you do it.
As to if they repent I'm not sure. I think if they repent they should see even more why they should be punished, but Jesus said when you're saved your slate's wiped clean. 
Paul was a blasphemer and he stood by and consented to Stephen's death yet he was completely forgiven by God and set to minister. It's how to have a good balance I guess, showing God's justice but His mercy as well.
1Ti 1:12  And I thank Christ Jesus our Lord, who hath enabled me, for that he counted me faithful, putting me into the ministry; 
1Ti 1:13  Who was before a blasphemer, and a persecutor, and injurious: but I obtained mercy, because I did it ignorantly in unbelief. 
1Ti 1:14  And the grace of our Lord was exceeding abundant with faith and love which is in Christ Jesus. 
1Ti 1:15  This is a faithful saying, and worthy of all acceptation, that Christ Jesus came into the world to save sinners; of whom I am chief. 
1Ti 1:16  Howbeit for this cause I obtained mercy, that in me first Jesus Christ might shew forth all longsuffering, for a pattern to them which should hereafter believe on him to life everlasting.