Dative case

Hi,

in 7.1 (Er ist in seinem Büro), why is the "buro" in the dative?

BR,
yahya

Because it involves being in a location.  "In" can also take the accusative if it is motion towards something.e.g. gehen ins Kino.  Similar prepositions that can take either dative or accusative are an, auf, hinter, neben, uber, unter, vor, and zwischen.  Where at a location, it's the dative, but if movement is involved regarding something associated with the location, it is the accusative.

Hallo Yahya, 

vielen Dank für deine Frage. 
As Flakkaserne correctly explained, the preposition "in" requires the dative case. Hence, "in seinem Büro".

Liebe Grüße, 
Leah von Rocket Languages