I would like to play a video from inside the rendered page with an iPhone/Safari.
When I put a <video>, it's always opened and played in a separate full-screen Quicktime window. Is there a way to play the video directly from the page?
(a similar question Play video not in full screen mode suggests it's not possible)
Yes, it's possible to play video within the browser, but as you said, in the Quicktime fullscreen application, and the HTML5 sound API is not available (in iPhone OS 3.x).
But in the coming iPhone OS 4, it will be possible (used for iAd), so you will have to wait until this summer (or play with the beta SDK now).