Question: Since we are part of Krishna, and since Rādhārāṇī is also part of Krishna, does that mean we have part of Rādhārāṇī in us?
Bhāgavatam explains that we are different parts. Rādhārāṇī is the what Bhāgavatam describes as bhakti-śakti, and we are what Bhāgavatam describes as taṭastha-śakti.
There is an intrinsic relationship between bhakti-śakti and taṭastha-śakti, however: the taṭastha-śakti can become an instrument of bhakti-śakti. So, we can become an instrument of Śrīmatī Rādhārāṇī.
Question: Why do some people say we have Bhakti in us, but it is dormant and we have to reawaken it?
Different people have different ways of expressing things. We are meant to be an instrument of bhakti-śakti – so one could describe that as having the dormant capacity for bhakti, and this capacity has to be awakened or realized.
Bhakti, however, is actually something much greater than us. We do not possess it. We are just hoping that it will possess us. We do not create it, we are just hoping that it will use us in its play.
Question: If Krishna is omniscient, wouldn’t he know what Rādhārāṇī’s love feels like? Why would he have to become Śrī Caitanya Mahaprabhu to experience it?
His omniscience will not interfere with his primary reason for existing – bliss. Just as we also can forget or ignore things that interfere with our enjoyment, he also certainly can. His omniscience is only a servant of his bliss. In the bliss of love, he experiences that Rādhārāṇī is someone whom he cannot fully fathom, and he joins with her as Śrī Caitanya Mahaprabhu to try and experience firsthand what she experiences.