NO YOU DONT. after 20-30 seconds (or less) of the arteries being cut, so much blood loss from the brain and you go into shut down mode real fast. still a bad way to go out.
yes you do and there is plenty of clips around that suggest quite the difference,
1) Chechnia 7 conscripts head cut off (you don't want to see that, but they were alife for a long time, one of the Terrorists even said to one who wanted to get back up... Look he's invincible)
2) Pleanty of iraq movies, were people don't stop fighting until their head is nearly off and they basicly drown in their own blood, you can hear the breathing for a long time.
in france back in the French revolution a doctor took the oportunity to document what would happen if people got guioteened, he took the head of the beheaded looked them in the face an shouted their name, and a lot of times their eyes would open and trust me you've seen the difference of dead eyes and alife one and once and you know the difference, he said they were concious.