What are the Sharia limits for interacting with non-mahram women in terms of looking, speaking, smiling, and shaking hands, and is shaking hands permissible in some cases?

It is advisable for the student to study in Muslim countries due to the corruption of religion and morals prevalent in non-Muslim lands. If the study involves something unlawful, such as impermissible mixing of genders, then it is absolutely forbidden.

As for interaction with women: 1. Handshake: It is permissible to shake the hand of an elderly woman who is past the age of desire and not desired, as long as there is no fear of temptation. However, shaking the hand of a young woman is forbidden by the consensus of the four imams. 2. Gazing: Jurists have agreed that it is impermissible for a man to look at anything of a woman except her face and hands. They differed on the permissibility of looking at the face and hands; some permitted it when temptation and desire are absent, while others forbade it even if temptation is absent. 3. Conversation: It is permissible to converse with a non-mahram woman for a legitimate need, subject to Sharia-compliant controls such as the absence of seclusion, absence of suspicion, and avoiding soft speech, and that the conversation does not exceed the extent of the need. It is not permissible without a need because it is a potential source of temptation.

One must follow the commands of Allah and His Messenger, and pay no attention to what people say.