Old Youtube add-ons will not work anymore because Youtube changed its layout. I've never been offered 'classic view mode', but you can be pretty certain that all add-ons that display buttons on Youtube must be updated sooner or later in order to work correctly, no matter which mode you're using.
The 'Get Add-ons' panel has been removed from TenFourFox because new add-ons are not compatible with the browser anymore. You can always go to http://addons.mozilla.org/ and install the last compatible version (scroll down to 'See all versions'). I see that this won't help you with Youtube, sadly. If you want to download videos, you can use http://en.savefrom.net/ or any other web service.