How have Romeo's dreams and premonitions intensified the work of fate?
The dream Romeo has actually comes true by scene 3. He starts with these joyful word that indicate he is about to get some joyful news... and he is about to get news, it just happens to be sad:
If I may trust the flattering truth of sleep,
My dreams presage some joyful news at hand:
My bosom's lord sits lightly in his throne;
And all this day an unaccustom'd spirit
Lifts me above the ground with cheerful thoughts.
What could be fate her is that he has this spirit lifting him almost into another world, like a heaven, that can only happen to people when they die, something he is closer to than he realizes.
Further, a stronger truth develops that we do see in Act V, scene iii for sure:
I dreamt my lady came and found me dead--
Strange dream, that gives a dead man leave
And breathed such life with kisses in my lips,
That I revived, and was an emperor.
She will find Romeo dead, and she does kiss Romeo's lips after he has taken a poison in scene iii. That kiss was likely the last human feeling he experienced that escorted him into the next world making him feel an emperor.