Learn German: Kann er das Bild malen? - Can he paint the picture?

The verb können (to be able to / can) is a modal verb. Modal verbs are irregular in their singular forms (I, you, he/she/it). For er (he), the vowel changes from 'ö' to 'a', and it does not take the usual '-t' ending you might expect. So it simply becomes er kann.

Why is malen (to paint) at the very end of the sentence?

This is a great example of the German sentence bracket (Satzklammer). When you use a modal verb like können, the modal verb gets conjugated and takes the main verb slot (here, position 1 for a question). It then kicks the second verb (malen) in its basic dictionary form (infinitive) all the way to the end of the sentence.

Why does the sentence start with the verb Kann?

Because this is a yes/no question. In German, just like in English, you form a question that can be answered with "yes" or "no" by moving the conjugated verb to the very first position. The statement Er kann (He can) flips to become the question Kann er (Can he).

Is das Bild in the nominative or accusative case here?

It is in the accusative case because it is the direct object, meaning it is the thing receiving the action of being painted. The subject doing the action is er (he). Because Bild is a neuter noun, its word for "the" is das in both the nominative and accusative cases, so it looks exactly the same either way.