The correct sentences are:
Er kommt mit seinem Auto (=Dativ).
Ich kaufe sein Auto (=Akkusativ).
Please note that "Auto" is a neuter noun in singular. When you use, for example, "VW" instead of "Auto", you have to use the masculine variant.
The first sentence uses Dativ, because the preposition "mit" requires that case. When studying German, you have to learn by heart for every preposition which case(s) they use.
The second sentence uses Akkusativ, because the verb "etwas (=Akkusativ) kaufen" (to buy something) requires this case. This construction can be expanded a bit to "jemandem (=Dativ) etwas (=Akkusativ) kaufen" (to buy something for somebody) but the dative object is not required. For every verb the case(s) they use must be learnt by heart. There are some rules of thumb: For example with verbs like "jemandem (=Dativ) etwas (=Akkusativ) geben" (to give something to somebody) that have two objects, the Dativ is used for the receiver and the Akkusativ is used for the object that is given. But that's only a tendency and you are better off learning the cases for every verb by heart.