What is the ruling on a suitor communicating with his fiancée via Facebook, and what are the Sharia-compliant guidelines for her going out with her sister's husband to arrange family matters?

Your fiancée is a stranger to her sister's husband, and he is not one of her mahrams. Therefore, she must observe hijab in his presence and avoid being alone with him or speaking to him without necessity. Adding men on Facebook, or vice-versa, is permissible merely for viewing public posts, but private chatting is not allowed. Adhering to Sharia is not blameworthy extremism, and one who adheres to the religion should be wise and gentle with those whom they invite and guide.