Good question!!
I've been wondering about this for a long time as well, and below are my (perhaps crazy) thoughts.
While some of her knowledge of the future seems to be based on having experienced previous iterations of the matrix, I think that some of these "predictions" may instead be an attempt to INFLUENCE the future. Remember when she first "baked Neo's noodle"?? -- it was when she told him not to knock over the vase, and then when he did, she asked him to think about whether he would have done it if she hadn't told him he would.
Perhaps the Oracle telling Trin that she would fall in love with The One was an attempt to MAKE it happen.
Yes, it is possible that Trin would have fallen in love with him anyway, but I bet she paid a lot more attention to Neo once the Oracle told her this, making a relationship more likely. Remember, the first movie starts out with Cypher giving Trin a hard time for "liking" him while they are preparing to make contact, i.e., she hadn't even met him yet.
My take on it is that the Oracle tried to encourage the relationship between Trinity and Neo to force a change in the cycle of the matrix "because what she is interested in is the future". Remember, at the end of Revolutions, Archie tells the Oracle something along the line of "you are playing a dangerous game", suggesting that she is manipulating things and that neither she nor Archie really knows what is going to happen as this game proceeds. They both make predictions based on probabilities, but neither can "see past the choices they don't understand". In other words, they can't calculate probabilities if they don't know the variables or the equations relating the variables.
I think that what the Oracle is doing in all of her apparent seeing of the future is predicting outcomes based on her combined understanding of The Matrix and human nature. She sees that IF The One falls in love, he will make a different choice than previous Ones. She sees Neo's and Trin's personalities (via the Matrix) and can predict that they will be compatible. She tells Trin that she will fall in love with a man, and this man will be The One, in an attempt to make sure that this happens.
Based on this reasoning, I don't think that she can make any detailed predictions about anyone who has not been in The Matrix, but her understanding of human nature should allow her to make predictions about us as a group.
Here is another point that leads me to the conclusion that the Oracle is not "seeing" the future but instead "predicting" it and trying to manipulate it: why would the Oracle tell the humans her visions of the future, except to influence the future???