If I delete an item in the activity stream, am I also deleting the associated record for the contact, task, event, project or opportunity?

No, you are simply removing it from the activity stream, but the record remains in its respective location. For example, if you remove an item in the stream that says, “Wealthbox user Bill Smith added a new contact named John Doe,” the stream item would be removed but the contact record, “John Doe,” still exists and can be deleted on that contact record page.