In order for people to edit data, they have to be collaborators or you have to use a 3rd party integration. With a 3rd party integration, people can edit data without being Airtable collaborators.
Everyone who is a collaborator can see all the data in the base.
Everyone who is a collaborator with edit permissions can edit all records in all tables in the base, unless you have a Pro subscription and use field and table editing permissions to restrict what they can edit. The user will still be able to see all the data.
If you are on a free plan, you will be able to add someone else as a collaborator, but any collaborator will either have edit permissions for the entire table, or not edit permissions at all. On the free plan you cannot pick and choose which tables/fields a user can edit.
If a person makes changes to a linked record, those changes are reflected in the lookups and rollups in the linked table.
It looks like you will need to make some decisions:
stay with the free plan, add the user as a collaborator with edit access, and trust that the user will not edit data that you do not want edited
pay for a 3rd party integration (but not add the user as a collaborator) You would have ultimate control on what data the user could see and edit. However, the user would not be using the Airtable native interface.
pay for a pro subscription. The other user could see all the data in all the tables, but you could limit editing to specific fields in specific tables.