we definitely could have done a better job at indicating what you can and can't do.
The axe isn't used for cutting down trees it's only there for combat, and the planks you find are used for building, when you place a planter box you should see an icon above it showing the materials required for construction and how many.
The bottles are health potions that are only required when in combat, if you explore a bit more you should find a build site which will unlock the bridge into the second area, enemies only spawn after unlocking that bridge