Youtube – YouTube URL parameter for continuously playing without timing out

You must be doing something wrong, here's the right way to share YouTube videos on Facebook wall, go to that video page on YouTube that you want to share, then click on Share button, you'll see a Facebook icon there, click on that icon, a small pop up window will open, Facebook will ask your login details, if you are already logged in Facebook then you'll see your video embedded in a post, just give a title to your post and then you'll see your video posted on your wall rather than links :)

The playlist is available in the current design (One Channel, which you're referring to as "new design") if the user has featured a "newest video" shelf on their channel page – click the "play all" button.

In the now-new design (Material Design), there is a link to play all videos on the /videos tab of any channel.