Thee Oracle is basically a program & she has been their & witnessed all 6 cycles of the matrix, if you believe what the Architect said near the end. 1 percent of all people will not acept the program or matrix & Neo is an anomaly. With that in mind think about what the Oracle said to Neo the first time they met: Neo - "I'm not the One" Oracle - "Sorry kiddo, you got the gift, but it looks like your waiting for something." Neo - "What?" Oracle - "Your next life maybe.. thats how these things go."
The Oracle had probably met Neo there for the 6th time & she remembers all previous visits. That makes more sense now when she said to Neo about breaking the Vase. Neo - "How did you know" Oracle "Whats really gonna bake your noodle later on is would you have still of broken it.. if I hadn't said anything."
Seraph is another program designed to protect her location in the matrix. How he can tell who is good & evil by fighting them is beyond me though.
Indeed - The proficy is true & Neo lied to Morpheus.. knowing he had a choice to save Trinity through one door OR save Zion & destroy the Matrix.. well he could have choosed the door to save Zion instead. Lied might be too strong a word, maybe Just didn't tell.