Should it not be 日本へ行きます
I don't think so; the particle "へ" there means going toward Japan. (I think).
Yeah, it can be either. へ Is still used even for a proper destination sometimes. I think it makes sense for the future tense because while you might intend to go to Japan, you might still change your mind.
It can be either へor に
Yeah me too
What would be wrong with 「来年日本にわたしは行きます」?
It took it fine, for me. It's just one of those sentences where they want you to use Hiragana for 私 for no reason, despite it being implied. As far as I can see, anyway...