Is a husband’s fast affected if he kisses his wife during the fasting hours? And does having a wet dream during fasting invalidate fasting?

A wet dream does not invalidate a fast; in fact, it has no effect on fasting. The person concerned should take a bath or shower in the normal way, by washing all his body with water before sunset if possible. His fast remains valid if he wakes up close to the time of sunset or if he does not have the facility to take a shower until after the fast is over. What is important to know, is that a person has no control over wet dreams. As such, it cannot affect his voluntary action of fasting.
The Prophet (peace and blessings be upon him) said: "A kiss does not invalidate fasting or ablution." However, a man must refrain from kissing his wife with desire during the fasting hours because we are required to abstain from food, drink and sex while fasting.
Aisha (may God be pleased with her) was asked whether the Prophet (peace and blessings be upon him) kissed his wives when he was fasting. She answered: "Yes, but he had the greatest control over his desire among you.”
And God the Almighty knows best.