There are many different theories about time travel, but my guess would be that if you time travel and stop something from happening. A different timeline would open up, one where you didn't stop it; and one where you did. Then in both timelines you'd live out your lives. One where whatever you stopped got stopped successfully, and one where you will live your days with whatever you tried to stop.
Also I believe that the timeline where you went back in time would be erased so it would not loop, like how you said. If you successfully stopped it, then that person would not exist anymore and you'd basically replace them upon your return.
The truth is nobody on this planet, I hope, knows for sure. So its really hard to actually think about what would happen because its such a vast topic. It's more up too what you believe would happen! :)
If they are children of slaves then they usually are. If they are capture slaves then they might not be. It really depends on when and who their parents are. There is no definite answer. Hope this helps;)
