Relationships are handled throughout Chimpegration Classic as long as the MailChimp list is configured in Chimpegration Classic settings to handle relationships. A list should have a column that represents whether or not a record is a constituent or a relationship (referred to as the record type merge field). The constituent id column for a relationship is populated with the relationship import id (rather than the constituent id).
In export you can select either a constituent or a relationship query to export data to MailChimp. You need to map the relationship import id to the MailChimp merge variable that represents the unique id (otherwise this would store the constituent id). Otherwise export behaves the same way. You can read about export on this page of our User Guide.
In manage campaigns, the email address is looked up on the either the constituent or relationship depending on the type of record that is stored on that MailChimp record (as determined by the record type merge field). Because Chimpegration Classic is working with relationships, there are a limited number of actions that can be taken but it is possible to perform the same actions on emails as with constituents and also add a relationship attribute too.
Synchronisation has its own module for relationships as this really is the most complicated of areas. The functionality is not as great as the regular sync but nevertheless gives you the opportunity to sync relationship data between RE and MC. It is not possible for new records on MailChimp to be created as relationships in RE but existing records can be synchronised. You can read about syncronising relationships on this page of our User Guide.
Finally you can remove records from a MailChimp list based on a query. Here you would need to select whether to remove constituents or relationships based on respective queries.