I don't know for sure, but I am thinking a chocolate ganache would work for the drizzles? Or maybe chocolate melted and drizzled with a piping bag to control more uniform 'dripping?' And I would think any chocolate buttercream or chocolate cream icing would work for the rest...am curious to see what others say.
You can use any chocolate buttercream to ice the cake. I would suggest chocolate ganache for the drizzles. There are lots of recipes for that too, but it is basically chocolate and heavy cream. When I am just doing the drizzles, I like to put mine in a large squeeze bottle (Hobby Lobby, Michaels, etc) so that I have more control.
If you want specific recipes, PM me and I'll give you my suggestions.
I also saw some videos on youtube to show how to drizzle the ganache down the sides like that.