The 14-letter word that means to go around something is "circumvent." It refers to finding a way around an obstacle or avoiding an issue, often by clever or indirect means.
One answer could be "chair" (hair, air).
A four letter word meaning the foundation of something is base.
A ten letter word for something that occurs could be an occurrence or happenings.
have
The word that means to search through something by moving things around is "rummage."
Urge
An Acrostic
lose
Improve
Own
have
shard