Flash is headed for irrelevance - I doubt it will make much difference at all in this format choice. What will matter a lot more is what format mobile devices are able to play.
Other than some minor annoyance of flipping to Chrome, the only real downside to browsing without Flash is that there's a surprisingly number of sites that silently fail without warning if you don't have flash installed. I'm looking at you, eBay.
I'd love to uninstall Flash, but it'd be a major pain if I had to switch over to Chrome every time I wanted to visit an MP3 blog or news site (think CNN or The Verge with their proprietary Flash video players).
EDIT: Also, last I checked, HTML5 videos on YouTube could not be played in "true" fullscreen (they'd only take over the browser window, not your entire screen). Has that changed?
2) Yes, full screen works since the JS API was implemented in all browsers (albeit prefixed until recently) except for IE.
Most browsers (at least Safari definitely does) do proper full screen too.
I'm not sure if the experience would be as good with Firefox as I'm not sure if they support H.264 yet. But I heard that was planned.
I'd encourage you to try it for a while - it's free and pretty quick to re-install Flash if it gets too annoying.