Hello Brax1008
I had to use a converter to know the dimensions, since we do not use inches in Europe but centimetres (43 X 25 × 68). There are baggage racks on the train as well, or you can also put it between the seats. I doubt that it will fit on the hat rack, it depends on the car type. There is no limitation regarding hand luggage; the only requirements: you must be able to load/unload it yourself, and it must not block entry doors and aisles.
My advice: travel light whenever possible, it will ease your travel.
Best regards,
Roland