I cannot open many chests in the Spellbound Caves. These are the chests that have a sand block on top of them and a sign saying what is in the chest.
Is this by design? Is there a way to unlock them or open them?
If your in adventure mode then yes you will need to switch to survival.
The maps were originally designed for survival, the map you are playing is one of his early works and may need updating to be fully playable in adventure mode.
Vechs maps are open to play however you want with only a few basic rules (No crafting wool for the monument), they are not like the maps that have very specific rules about breaking blocks.