Lord Chaitanya: Reference to Lord Chaitanya in Scriptures

Q. 1. I'm confused on the subject of yuga avatars in this cycle of Kali. Gaudiya Vaisnavas claim Sri Caitanya Mahaprabhu as the avatar for this particular cycle of Kali yuga. Since he has already appeared, will this kali yuga end without the appearance of the Kalki avatar? This seems to contradict the Vishnu Purana.

Q. When I talk to someone about god I usually talk about Krishna. But when I say Mahaprabhu is also Krishna Himself, they get confused and then I tell them that Chaitanya Mahaprabhu is Krishna Himself. But the thing is I don't know how to answer them properly and I think I make them more confused.

Q. Why is Sri Chaitanya Mahaprabhu not mentioned in the Srimad Bhagavatam First canto, where all other incarnations are included?