Note, while I have taken Homicide Coursework in the distant past and have a few years as a Accident Investigator by way of Insurance Fraud investigations these are just my informed opinion based on schooling and work from 20+ years ago.
a) if a body was beheaded pre- or post-mortem and
Yes. Take the head off while they are living and you will have blood EVERYWHERE. Dead it will puddle around the wound at best. This one you can figure out at the scene just by looking.
b) if someone bleeds to death, how quickly they did so?
Again yes, but you would want a experts opinion on the wound and blood flow rate.