Yeah, normally I'd recommend a trench coat or something like that, but if you're shorter you may want to stick to a shorter coat - maybe look at Barbour coats. Padded "farmer" type coats, very big over here in the UK at the moment. Some of them look very stylish, some of them look a bit too countryside. But pick well and you're good to go.
On the scarf issue, be careful how you wear it. I would avoid wrapping it around your neck, as this separation between body and head could make you look shorter as well. Keeping it draped longer without the wrap around would elongate everything a bit more.
Look interesting, have seen some with a belt on the waist, would you think that would look feminine though?
Another good one thanks, unless the coat also covers the neck I might need to wrap it otherwise it won't cover the throat, the weakest part, but same colour as the coat could minimize the issue.