¿Why not ‘Is post secundam horam prandium coquit.’?
It works too, however in practice it is much rarer, because "is" isn't really a pronoun, there are better options even in cases of emphasizing the subject of the sentence.
Isn't it the same as "Post secundam horam ille prandium coquit" since "ille" can be translated as "he"? Actually, the "ille" can be used to emphasize the doer.
Yes, I believe so - "Is" correct also.