No, it doesn't. If it did, buildings in NYC would be falling down left and right. Heck, I hear they even put them under entire bodies of water!
Yes, tunnels can flood, if they are below the water table. Good pumps can fix that problem. Again, the Chunnel being Exhibit A - it hasn't flooded, yet.
Yes, but in those cases the tunnel structure itself ends up taking up load previously carried by the material that's removed. That is why the walls of the tunnel are shored up with reinforced concrete rings, which provide mechanical support AND keep out water. That's why we have tunnels that are bored only a few tens of feet in the mud under deep bodies of water, and yet don't collapse or flood.
Yes, tunnels can flood, if they are below the water table. Good pumps can fix that problem. Again, the Chunnel being Exhibit A - it hasn't flooded, yet.