An even more useful reminder than my earlier one: the fields that FreeCRM uses to import (e.g.) the company for a contact are the text identifiers set by the user, not the internal database IDs. Don’t chose Company Name (creates new) or Company System Id record merge, just the Company Identifier.
That said, to add additional information (e.g. identifier) to a company, you definitely need to use the numeric internal ID and chose the “merge” option when offered it in the import mapping drop-down.