Well, ( 1. ) is only valid to a certain degree. Void Lords are also associated with madness and dark magic has long been associated with tendrils. As such, Shadow Priests actually aren't particularly Old God themed. Of course our Artifact unquestionably is, but a claw of an Old God would make an excellent channel for Void powers by its very nature.
Aside from a few talents, and reminding everyone that one talent is actually called "Void Lord", very little of it is exclusively Old God in nature.
And no. Shadow Priests don't have to go through the Old Gods to wield Void magic. Void magic is omnipresent and within everyone, so you only need to go through yourself. I'm sure you could bargain with more powerful entities for a boost, but it's far from necessary. However, the powers of the Void have long been shown to have the power to madden and corrupt if not handled with care, so there's that.
EDIT: Hell, the current "Surrender to Madness" text doesn't even mention the Old Gods anymore!
http://legion.wowhead.com/spell=1932...der-to-madness
They outright removed the bit about selling your soul to the Old Gods. They even took away Xal'Atath's ability to summon Faceless Ones!