Learn Russian: Шпион притворился наивным мальчиком.

The verb притвориться (to pretend to be) requires the Instrumental case for the role or state the person is adopting. This is often called the Instrumental of manifestation. When you pretend to be someone, turn out to be someone (оказаться), or remain someone (остаться), Russian uses the Instrumental to show that temporary or adopted state.

In English we say 'pretended to be'. Do we ever need to add быть in the Russian sentence?

No, you never use быть after притворяться or притвориться when followed by a noun or adjective. The meaning of 'to be' is already baked into the combination of the verb and the Instrumental case.

Why is the verb притворился reflexive (ending in -ся)?

Think of the -ся particle here as acting on oneself: the spy is making himself appear as a naive boy. The verb for 'to pretend' (притворяться or притвориться) is always reflexive in Russian.

Could we use the imperfective verb притворялся instead in this context?

You could, but it would change the meaning. The perfective притворился implies a single, successful, completed action (he pulled off the act in that specific situation). The imperfective притворялся would mean he was pretending over a period of time, or that he regularly pretended to be a naive boy.