Other

You must give it to the person you took it from. If you don’t know him, give it in charity.

No problem in shopping and buying halal products.

This is cheating and is not permissible. If you must study these subjects, study to pass the exams without believing in it.

If you do your best to lower your gaze and don’t intend to gaze in sha Allah, you are not sinful.

You can change your first name but it is not obligatory unless it holds haram meaning. You must not be called after anyone except your father’s name and your family name.

It means, ‘As Allah the Almighty has willed’.

If you are a man and it is safe where you are going, No problem in this.

This is baseless.

Your islam is valid if you are sincere. However, no one can treat you as a Muslim until you announce it. If you die, they will give you Christian burial with the disbelievers. Trust Allah and choose the right moment and announce your islam and Allah will take care of you.