The things that can be deduced about the relationship between when Jem and Scout call their father by his first name is that Atticus do treat his children well and make them his friend.
The relationship that exist between Atticus as well as his children can be seen as a cordial relationship because he made his children to be his best friend and always give them the respect that he can give the fellow adult.
In conclusion, there was an uncommon bond existing between them, which make him to be able to play very well with him, hence things that can be deduced about the relationship between when Jem and Scout call their father by his first name is that Atticus do treat his children well and make them his friend.
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