Sort of. In Vinge's world, the slow zone is just a natural phenomenon, not something artificially created. And in the slow zone you're basically limited to nearly-speed-of-light travel consistent with our contemporary understanding of relativistic physics (which is unbearably slow to anyone who can travel much faster than that outside the slow zone). Whereas in Liu Cixin's books, if I remember correctly, they actually change the speed of light itself to be even slower.
If I remember correctly, there's some ambiguity whether the slow zone was created by some power or naturally occurring (or a bit of both) although a bit of both is perhaps the natural answer.
You may be right; it's been a long time since I read A Fire upon the Deep or A Deepness in the Sky.
I remember some insinuations to that effect, but from an unreliable narrator given Vinge's penchant for strictly in-character exposition, and what would child races know of progenitor's motives?
As a universe arrangement scheme (both narratively and literally), it is a clean solution to providing a new race incubator and preventing "Why don't the First Ones rule everyone?" endgames.
Sounds similar (I still need to read Liu), but in Vinge, it wasn't light speed being reduced, it was a variety of limitations on superluminal physics, computation/intelligence, and maybe even physical properties. (variations in quantum physics, perhaps)