Long Island is a big place. The water table ranges from virtually nothing on the barrier islands to the south, to 70 feet on parts of the North Shore. See here to check for your location.

Self-healing foundations? Love the idea! But no.

Doesn't sound like much leakage though if this is not a finished basement and water isn't accumulating somewhere behind finished walls before revealing itself on the floor.

Check:

--Grading

Ground should slope away from the foundation.

--Eavestroughs

Eavestroughs (gutters) should be sloped gently to the downspouts and must be large enough and clean enough so that water flows to the downspouts.

--Downspouts

Downspouts should bring the water at least 10 feet away from the wall.

Too many of these just dump the water onto the ground two or three feet from the foundation.