What is the ruling on the aforementioned action taken by the wife, who took her friend's husband's email address and added it to her contact list to communicate with her, and sent a message to her friend's husband when she was unable to reach his wife?

It is feared that sending an online message to your friend's husband without your husband's knowledge could be a step of Satan that might destroy your life and disturb your relationship with your husband. You must be cautious not to repeat this except with your husband's knowledge. The general rule is that it is permissible for a woman to ask a non-mahram man, or vice versa, about ordinary matters. We advise you to delete the email address of your friend's husband or any other man, and to stay away from situations of suspicion, for the Prophet, peace and blessings be upon him, said: "Indeed, Satan flows through the son of Adam like blood, and I feared that he might cast something into your hearts."