Yes, no/yes, and yes, would be my understanding. This of course assumes that we’ve magically attached all of the nerves correctly. No to the part about the senses since what is happening is the doctor is essentially attaching a new blood supply to a severed head that’s been put on ice, so the head-based senses like scent and sight are unchanged. I’d expect the sense of touch and pain to translate well since it’s a one-direction signal sent from the skin pressure sensors to the brain. That’s a simple enough signal processing task that wouldn’t change though the brain would probably have to get used to what sensations correspond to which part of the body. The bi-directional senses like knowing where your limbs are in space would be atrociously tough to recalibrate. That leads me to my Yes answers, because our brain would have an incredibly tough time recalibrating it’s ability to communicate with the body. This is similar to a victims of nerve damage that, after repairing the damage, have to learn how to walk all over again. The message is getting through but it’s a completely garbled mess and the two sides have to re-establish communication.
That was a fun thought experiment. Hopefully it answered your question. I’d love to hear your thoughts.