Are entity IDs assigned per entity or across the board?
Each entity type has it's own ID sequence. For example a user may have the uid of 1 while a node may also have an nid of 1. Similarly a taxonomy term may have a tid of 1. In all those cases the "entity_id" is 1.

Regarding the serial module, as it provides a field via the Field API, presumably that field could be attached to any entity bundle.

In regards to linking your entities, you could probably use the entityreference module to create reference links between your entities.