×In Remote Forest Town: Twice South, Once East, you'll need to step on the arrow rotator token at (7,14).

×Pickaxe ain't really helpful for getting to NE part of the forest city.

You'll need water flippers. and you get them later in the hold.

You'll be able to return to Part IV later. And with flippers, the level is much easier to explore ;)

EDIT: as for your question about 2E - you'll need grappling hook to get past the pit. You get it in Part VI, too