that would be a kind of mud wasp, i suppose? they anaesthetize the spider, drag it into their mud nest & lay their eggs in or on it, so their offspring feeds on the spider. i see them around here all the time.
Yes, they paralyze the spider. I don't know what species these are. They're very small but powerful. I've seen them lop the legs off spiders too, all Boxing Helena style. This was the 2nd time I've caught this in action,but with a better camera.