1- There is no atonement for adultery, but it is a deadly (kabira) sin. The best way is first to repent of it truly and then to ask Allah for absolution (without revealing it to any person). 2- In mentioned cases neither stoning nor lashing are as punishment. Suppose a permanent marriage between a man and a woman in which one of them has sexual intercourse with other men and women. If four fair men testify in a court of law that they have witnessed that affair or man or woman themselves confess (in a way that they are not enforced) four times, as a result stoning in Islamic law is legal. Lashing is legitimate in the cases other than adultery (as it is explained in treatise for zina mohsina). Kissing and hugging are not punished with stoning nor lashing (there is just ta'zir if it is proved by a judge), otherwise repenting is enough.