There is nothing wrong with cutting nails or shaving the pubic hair while fasting.

A man may kiss, hug and touch his wife without having intercourse when he is fasting. But if there is the fear that he may do something that Allah has forbidden because his desire is aroused quickly, then it is disliked for him to do that.

You should not delay ghusl after having sexual intercourse with your wife in Ramadan so that you can pray Fajr with the congregation in the mosque.