#God said to him

"God said to Abimelech"

#in the integrity of your heart you did this

Here "heart" stands for his thoughts or intentions. AT: "you did this with good intentions" or "you did this without evil intentions" (See: [[:en:ta:vol2:translate:figs_metonymy]])

#to touch her

This is a euphemism for sleeping with Sarah. AT: "to sleep with her" or "to touch Sarah"  (See: [[:en:ta:vol2:translate:figs_euphemism]])

#the man's wife

"Abraham's wife"

#you will live

"I will let you live"

#all who are yours

"all of your people"