With Roman legions taking slaves from defeated enemies (Caesar alone taking half a million in Gaul). How did people trust the slaves when they bought them?
Say that I bought a Gallic woman as a slave to cook and clean in my household. She is from a warrior tradition and in a house filled with knives and other cooking implements. I know I have the power of life and death over them but what if they didn't care? What if they were willing to die whilst getting revenge?
How do they trust their slaves? It seems an impossible risk to take.
This concern was very real to Roman slaveholders. There was all sorts of anxiety over the trustworthiness of slaves. They were often viewed as the "enemies within." So how and why did ancient Romans still enslave people if they didn't trust their slaves?
Before getting into that, I need to address some of your other points in the question. It is true that a large number of people were captured and enslaved in wars. These people would have mostly been ordinary citizens. Anyone like a warrior would be more likely assigned to manual labor. Slaves in that situation did rebel, not just in the famous Spartacus revolt, but also in two revolts on Sicily (during 140-70 BCE), which had many large farms.
But it's not that unlikely for an enslaved captive to end up in a household, nor for a slave of any origin to want to rebel. And so there were mechanisms meant to deter disobedience and murder.
First, it is important that a master has complete control over their slaves. Perhaps the warrior woman in your example doesn't care, but the average slave, who has relatives or other close relationships within the household, would be more likely to care. The master can harm those you care about, or more simply separate people through sale.
The biggest deterrent is what happens when a slave does kill his enslaver. It was expected that all of his slaves be killed as punishment, not just the offender. This rule caused an outcry when L. Pedanius Secundus was killed because he had so many slaves. The Senate debated whether they should kill all 400 of his slaves and decided yes. Tacitus gives the speech of the senator giving the decision: because Roman households now "comprise nations," "you will never coerce such a medley of humanity except by terror." It was decided that the Secondus household should be killed to set an example. This was meant to deter violence and encourage slaves to inform on one another.
Because of the threat of violence to everyone around them, slaves were more likely to attempt escape or to engage in small, everyday acts of disobedience, rather than outright murder the slaveholder. But sometimes they still did kill, and that possibility scared the Romans.