Not my style but very pretty none the less. Yes, a hem might be necessary and you can decide if you want to keep the train or not when you do that. As for hair, maybe consider half up, half down? Think about how you would normally style it when you dress up to go out and that is a good place to work off of. You should be comfortable and have a style that makes you feels like the best version of yourself.
I think it's a perfect dress for elopement and you look gorgeous in it! Once it's hemmed, it'll be just right. I think a half up, half down hairstyle would be good and match the "feel" of the dress and veil. Maybe just soft curls at the bottom part of your hair?? It'll be soft and romantic like the dress.