You just copy the embed code provided by the video provider such as youtube and paste it in your post.
yes Wordpress is slowly developing some great plugins for image Gallery and Video gallery also. You can just add videos by embeding the codes.
i have a premium theme which can do that, its specifically developed for video cms systems. Its priced at $50 so if you wanna buy it then buzz me with a pm.
You just make posts with the videos embedded in them. There really is no plugins needed (I know as I have one).
As far as I know Wordpress doesn't allow javascript or some other code in the posts. To embed video in post I'm using this plugin: http://www.jovelstefan.de/embedded-video/ (I have Wordpress 2.3.3)