Foundation damage.
tap roots
Cutting a tree's roots can harm it, but it may not necessarily kill it. The extent of the damage depends on the size of the tree, the type of tree, and how many roots are cut. In some cases, cutting roots can weaken the tree and make it more susceptible to disease or other stressors, which could eventually lead to its death.
A Banyan tree grows roots from its branches and trunks; these roots are called Aerial roots.
Primarias
cypress trees
Tree roots are strong and can withstand significant forces. Factors that contribute to their strength include the type of tree, soil conditions, depth of the roots, and the presence of supporting structures like rocks or other roots.
The roots of any tree can pose a danger to building foundations, Fig trees can be quite large, but it'll depend on the proximity to the building and, presumably, the type of soil and the foundations. There are structural engineers who can survey the property and advise of any serious risk.
The roots of a Douglas fir tree absorb water and nutrients
Palm trees have fibrous roots, which are shallow and spread out widely from the base of the tree to anchor it in the soil. These roots are important for stability and absorbing nutrients and water.
Apple trees have a tap root for stability and fibrous roots to gather water. Apple tree roots do not grow when the tree buds. Then the roots are too busy gathering water and nutrients to grow more roots. After the fruit is grown, the roots will start growing again.
The type of tree you are referring to is likely a Bald Cypress tree. These trees have unique "knees" that protrude from the ground around the tree, resembling stumps. These structures are believed to help with oxygenation of the roots.
Tree roots can vary in depth depending on the type of tree and soil conditions, but they generally extend 2-3 times the diameter of the tree's canopy. The depth of tree roots can impact the surrounding environment by stabilizing soil, preventing erosion, and influencing the availability of water and nutrients for other plants.