I am certain that cats can and do kill chickens. Maybe not every cat will, and certainly not every chicken is at risk. But cats can kill chickens. Especially chicks, bantams, and oblivious birds like silkies.
However, it seems unlikely that it was a cat that killed your silkie, they usually don't remove heads but instead go for the soft or meaty parts like bellies & legs.
You're under no obligation to keep this cat you trapped, even if it is friendly or attractive. Contact your county's animal control department and find out their policy on found cats. It could be someone's lost microchipped pet and they can reunite them. Continue to keep the trap set & baited each night, perhaps try some sweet bait that won't attract more cats.