Where are Counterwallet account aliases and watched addresses stored?

They are stored on the Counterwallet server and hence not “portable” across different Counterwallet instances that are hosted by different entities.

On counterwallet.co aliases multiAPI() is used to store those on clustered Counterwallet server farm (cw0[1,2,3].counterparty.io) and multiAPINewest() is used the read the most recently stored alias value.