What are these weird 1 wide vertical tunnels?
Solution 1:
These are enchanted sword shrines.
A Shrine is marked by a long, narrow vertical shaft that may reach the surface, and features a small hill with Flower Walls and pools of water on either side. The breakable sword sprite rests atop the hill.
If you are lucky (33% chance), you can find an Enchanted Sword or Arkhalis in there, which are pretty nice if you get them early in the game.