You can ask this question with either 'yet' or 'already', but the meaning is different. 'Has the train arrived yet?' is a neutral question. You have no idea whether the train has arrived or not. You might say 'Has the train already arrived?' if you were expecting the train to arrive in, say, ten minutes' time, and - to your surprise - somebody tells you that it has arrived early. 'Has the train already arrived?' is a way of checking the surprising information. Similarly, if you ask 'Have you finished your homework yet?', this is a genuine enquiry and a neutral question. But if you were expecting your friend to take an hour over his homework, and he finishes after only half an hour, you might check that this is true by saying 'Have you finished your homework already?' meaning 'So soon?'. I hope this makes sense.

The correct way is has the train arrived yet? When you say has the train arrived already? It is a correct sentence but used when surprised let's say....wow has the train arrived already??