First one is definitely true and isn’t emphasized much and tbh I feel like that demand wasn’t unreasonable. Shipping people and things and providing defense would be a lot harder to an exclave than to contiguous territory. They did seriously overreact by invading, of course, and it seems like Mr H had some serious temperamental issues.
Second one I’ve never researched enough to know if it’s true or German propaganda.
I don’t recall the Germans ever claiming that Poland was about to invade them? Maybe I missed it.
Russians talk about further expansion too.