If I plan to use Skinny tables in my org, and say use it for accounts to improve performance issues, and as a result, set up say 30 fields in the skinny table, how do this work in the sandbox if skinny tables are not copied to a sandbox?
It's documented in Best Practices for Deployments with Large Data Volumes that
For Full sandboxes: Skinny tables are copied to your Full sandbox orgs.
For other types of sandboxes: Skinny tables aren’t copied to your sandbox organizations. To have production skinny tables activated for sandbox types other than Full sandboxes, contact Salesforce Customer Support.
The place you're most likely to need skinny tables for performance is in a Full Copy due to the data volume you can achieve in that environment.