Learn Icelandic: Keyrir hann frá sjúkrahúsinu núna? - Is he driving from the hospital now?

The base word is sjúkrahús (hospital), which is a neuter noun. The preposition frá (from) requires the following noun to take the dative case, which changes it to sjúkrahúsi. Because we are saying "from the hospital", we must add the definite article to the end of the word. For neuter nouns in the dative case, that ending is -nu, giving us the final word sjúkrahúsinu.

Why is the verb Keyrir at the very beginning of the sentence?

To turn a statement into a yes/no question in Icelandic, you move the verb to the front. While English often adds a helper verb (like "Is he driving?"), Icelandic simply swaps the subject and the main verb. Hann keyrir (He is driving) becomes Keyrir hann? (Is he driving?).

Icelandic doesn't have an "is doing" tense. How do we know to translate keyrir as "is driving" instead of "drives"?

You are right that Icelandic uses the same verb form for both "he drives" and "he is driving". Context tells you which one makes sense. In this sentence, the adverb núna (now) at the very end tells us the action is happening at this exact moment, so "is driving" is the most natural English translation.

Is sjúkrahús a compound word?