Annoyingly, I can't find any information online about such a simple guidance system. The earliest homing missile fielded by the Soviets was the K-13[1], which used technology reversed-engineered from the AIM-9 Sidewinder[2]. Later systems seem to be improvements upon that technology, not simplifications.
Yes, pretty much all early guided missiles of the sort were what's called "rear-aspect".
Can't see the plume - can't make a boom.