Learn Italian: Fai pulire la stanza al ragazzo? - Are you having the boy clean the room?

This is the core rule of the causative construction you are learning! Because the verb pulire (to clean) already has a direct object in this sentence, which is la stanza (the room), the person doing the cleaning must become an indirect object. We use the preposition a (to), which combines with il to form al. This avoids the confusion of having two direct objects in a row.

Can I change the word order to put the boy right after the verb, like Fai al ragazzo pulire la stanza?

No, in Italian, the conjugated verb (fai) and the infinitive (pulire) must stick tightly together. You cannot put the person doing the action between them. The standard order is fare + infinitive + the direct object + the indirect object.

Does fai mean you are forcing the boy to do it, or just asking him?

It can mean either, depending on the context. The construction of fare plus an infinitive translates to both making someone do something and having someone do something. In everyday Italian, it is often just the standard way to say you are arranging for a task to be done.

How would I say 'Are you having him clean the room?' using a pronoun instead of al ragazzo?