Learn Spanish (Latin America): Él nos deja ver la ilusión.

In causative structures with dejar and hacer, the conjugated verb and the infinitive (deja ver) act together as a tightly bound, single unit. Because of this, object pronouns must be placed before the conjugated verb (nos deja ver). You cannot attach the pronoun to the infinitive the way you can with verbs like querer or poder (meaning you cannot say Él deja vernos la ilusión).

Is nos a direct or indirect object in this sentence?

It acts as an indirect object here. The rule for causative verbs is: if the second verb (the infinitive) has its own direct object (in this case, la ilusión), the person being allowed to do the action takes an indirect object pronoun. Nos looks the same either way, but if the sentence were 'He lets him see the illusion,' you would clearly see the indirect object pronoun le in action: Él le deja ver la ilusión.

How would the meaning change if we used hacer instead of dejar (Él nos hace ver la ilusión)?

The verb dejar is used for giving permission ('to let' or 'to allow'), while hacer expresses causation or force ('to make' someone do something). Using hacer would change the meaning to 'He makes us see the illusion.'

Does only refer to a visual trick or literal 'illusion'?