What is the ruling on befriending foreign women from among relatives on Facebook, and what is the ruling on a comment or like from someone who uses a woman's picture next to their name, and is the one who sees this sinful, and what is the ruling on one who publishes some forbidden things but they are not dominant on their page?

There is no objection to adding non-mahram female relatives to one's friends list on Facebook, nor to the list including someone who publishes forbidden content, provided that one denounces such content. If someone comments and their profile picture is of a woman, you bear no sin, but you must avert your gaze from the picture and delete the comment to prevent men from seeing it. You also have a duty to explain the ruling on this matter to the person who posted the comment.