We have a coconut tree near the house. Can its root penetrate the underground foundation of my house?
This is very unlikely as the roots are meant for sandy soil and are fibrous and not very deep at all. Being fibrous, they would not wander far from the tree. I think you are safe.
This is supported here Coconut Tree Root System
Fibrous or adventitious root systems are a kind of coconut root system that consists of roots that are close to the surface of the coconut tree. For the sustainability of the coconut tree, an adventitious root system forms around the plant and a few roots reach deep into the soil. The number of coconut roots found on a coconut tree is proportional to its age. Coconut palm plants may be found all across the tropics, yielding big trees for landscaping, palm fronds for decoration, and coconuts for fruit and oil production. Sandy soils, high humidity, mild temperatures, strong sunlight, and consistent rainfall are all ideal for coconut trees to grow and mature. As per the Blue Planet Biomes, coconut palms thrive on or around coastlines to ensure that their shallow root system gets exposed to water. However, these trees can withstand exposure to saline water, as well.
What kind of roots does a coconut tree have, and why? The shallow fibrous root system of coconut palm trees draws water from the soil surface. Coconut palm trees have roots that grow just below the surface of the tree’s base in a fibrous mass, reaching out as far as the tree can be tall.