If you have a Y membership in a different St does it still work at other Y's nationally

Depends on their policy

Yes you can. The policy is you must go to the YMCA you belong to more often than your away YMCA

I believe that you can use another Y in a guest mode. I am not sure that you could use the facility for a lengthy period. I have been able to use to the Y in the Charlotte area for a week while visiting.

I used mine in Florida for a week.