"There is a bowl in the kitchen."
Translation:Da ist eine Schüssel in der Küche.
as far as i'm aware, "da ist" puts emphasis on the location of the bowl, while "es gibt" puts emphasis on the fact that the bowl exists with its location being additional information. so if someone were to ask if you had any bowls, "es gibt" would be more natural, but if someone were to ask what was in your kitchen then "da ist" would be more natural
Not all prepositions are dative. See https://en.wikibooks.org/wiki/German/Grammar/Prepositions_and_Postpositions
"in" is a preposition that can trigger either the dative or accusative case with the following object. When there is a change of location with the object (the object moves), then the accusative case is triggered (therefore a der would go to den and nothing else would be affected). However, when there is no movement of the object, the dative case is triggered and we know that with dative - Der becomes Dem, Die become Der, and Das becomes Dem. From this, the bowl did not move and hence the dative case is triggered - die Küche becomes der Küche. I hope that all makes sense :)