Examples of Immanence in Ramayana
#1)On page #13 "thereby also inaugurating Rama's life's mission of destroying evil and demonry in this world." Vishnu is the god of protection in Hinduism. Rama's life goal is brought on because he is the reincarnation of Vishnu. This immanence has no effect on the physical world; it only has an effect on the mentality of Rama.
#2)On page #27 Viswamithra says, to Janaka, "'How do you know it was not divine inspiration that gave you this thought.'" This statement indicates that Janaka's decision to use Shiva's bow as a challenge was immanence. No man other than Rama (as the reincarnation of Vishnu) would be able to use the bow of Shiva. Janaka deciding that this was the challenge a suitor had to overcome in order to marry his daughter was immanence. The divine relationship between Vishnu and Lakshmi dictated the decision that Janaka made. It did not directly influence the world it influenced the thoughts and decisions of Janaka.
Examples of Illusion in Ramayana
#1)Page #21 In Ahalya's story Indra takes the form of the sage Gautama. This is illusory because this is a direct physical manifestation of divinity meant to deceive.
#2)Page #15 In Mahabali's story Vishnu takes the form of a dwarf to deceive Mahabali. Vishnu is directly deceiving Mahabali so this is an example of illusion.
#3)Page #18 In Ganga's story Indra places the horse of Sakara behind the Sage Kapila. This was to deceive the children of Sakara and eventually lead to their deaths. This direct intervention of Indra to decieve Sakara's sons was illusion. He created the illusion that the Sage had taken the horse.