Let's take No. 2 first. HTML is a security risk and isn't such a good idea.
Let's see, No. 1: Just off the top of my head, you can post links to such like YouTube, but to embed a video, I am not sure I can even enable that in the ACP. And I don't have access to the cPanel here, so I couldn't add a script to allow the embedding of something like a flash video. Probably wouldn't get permission to allow it, anyway, because eventually it could lead to too much use of bandwidth.
But that's an interesting question and I can go over to my own site, which is also phpBB, and take a look in the cPanel and do some research. Or converse with the phpBB gurus over at their site. Back at you later on this.
EDIT: Seems that this might be possible if you have the BBCode for the video and paste the part after video/. Might not be necessary for me to change the permissions in the ACP for that to work, either. Still, I would need to try it to see if I have that correct. Interesting. I'll have to get back to this, though.
Freedom isn't free!