I would like to create 2 linked databases: Primary and Secondary.
In the Primary database I want to create a field that would be linked to the secondary database and once something is picked up from the validation list (e.g. from the appropriate field in the secondary database), all other fields will be automatically filled up with the same content as the identical fields in the same record (where the content for the linked field was picked up from) in the secondary database. I couldn’t find anything like that in the manual’s part about linking the databases. Please let me know if it’s possible at all in Inmagic.

If I understand correctly what you want to do, normally there would be no reason to do that. Once you have linked Primary to Secondary, you have access to all the other fields in Secondary, so there's no need to repopulate them in Primary. Instead you can just display them in Primary (on an Edit screen or a report), or you can search them, if you want to, by adding the Secondary fields to the search screen in Primary.