Robots I'm not sure, everything else would die, the Halo rings work by negating reality to temporarily erase the concept of neurologically complex life killing everything from trees that communicated through insects, to realities consciousness within the blast radius (the Halo universe is a living entity which had been infected by the Flood until the Halo rings cleared the infection).
The Halo rings ignore dimensional and temporal barriers allowing them to affect things even if they're in another universe or frozen in time. Possibly even negating reality warping but I'm not sure.
Halo rings wipe out every single living thing in the galaxy. Guardians couldn't come back because the traveller is dead. All vex would be killed and all hive would also be killed. What's left of the cabal and give gods would be destroyed by the foreunners
Traveller would've "lived" because it's not really alive in an organism way. Vex aren't really living, Hive would "live" because Hive Gods can just spawn more...literally.
There's no real proof in destiny that the traveller is alive or dead so I'll let it slide. But it's clearly stated that vex have biomass ( white goo) which would be destroyed, leaving them unable to function. And forerunners and easily superior to hive. They've destroyed and recreated the entire galaxy